Modeling Tribological Contacts in Wind Turbine Gearboxes

Modeling Tribological Contacts

In Wind Turbine Gearboxes

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and services

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Three Fundamental Capabilities

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DEPARTMENT OF ENERGY

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Sentient Science ServicesFundamental Capabilities

• Highly accurate reliability and performance predictions

• Holistic approach – considers multi-body dynamics, tribology, material science, and real world variability

Predict loads, life, and performance of complex

systems

Predict impact of feature level design factors on

component performance

Complete solution for optimal lifecycle

management of fielded assets


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World’s Most Tested Products


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Products with the Lowest Cost of Operation


Why do we model?

• Physical testing is expensive and time consuming• Physics-based models give us insight into the performance of

our bearings and gears through ‘virtual testing’

What do we model?

• Virtually anything • Does the model capture the relevant physics? • Governing Equations?• What assumptions have gone into the model?

“His method was inefficient in the extreme, for an immense ground had to be covered to get anything at all unless blind chance intervened and, at first, I was almost a sorry witness of his doings, knowing that just a little theory and calculation would have saved him 90 percent of the labor…” Nikola Tesla (1931), on Edison’s methods


What is Tribology?

• The science and engineering of interacting surfaces in relative motion.

• The study and application of the principles of friction, lubrication and wear

Source: Rexroth, Bosch Group

Main Bearing

Pitch Bearing

Yaw Bearing

Generator BearingGearbox Gears and Bearings

Yaw Gear


Figure 1: Spall propagation for a cylindrical roller bearing (SKF NU1012ML) under radial loading.

Rolling direction is right-to-left. Test ID#: DP0018-TS03 [7500 lbf , 6000 RPM]

1 2 3

4 5 6

7 8 9

10 11 12

• Three Phases of Growth– Incubation– Propagation– Accelerated Growth

BackgroundContact Fatigue


Stribeck Curve


Elastohydrodynamic Lubrication

Lubricant Pressurization

Surface Deflection

Piezoviscosity

Lubricant Flow

Surface

Deformation

Science Applications


Lubrication Assumptions

xFz

u

y

u

x

u

x

p

z

uw

y

uv

x

uu

t

u

2

2

2

2

2

2

yFz

v

y

v

x

v

y

p

z

vw

y

vv

x

vu

t

v

2

2

2

2

2

2

zFz

w

y

w

x

w

z

p

z

ww

y

wv

x

wu

t

w

2

2

2

2

2

2

Navier-Stokes Equations (Incompressible, Constant Viscosity)

2

2

z

u

x

p

2

2

z

v

y

p

0

z

w

y

v

x

u

Governing Equations

• Gravitational and inertial forces are negligible• Pressure is constant across the film• Lubricant flow is laminar• No slip at the boundaries• Film thickness is small compared to other dimensions• Newtonian lubricant


221212

33

th

y

hv

x

huww

vvh

y

uuh

xy

ph

yx

ph

xaaba

baba

WedgePhysical Stretch dgeDensity We

222 x

huuuu

x

h

x

uuh baba

ba

Poiseuille:

Flow

Direction

Poiseuille:

Cross-Flow

Direction

Couette:

Flow

Direction

Couette:

Cross-Flow

Direction

Normal

SqueezeLocal

Expansion

Translational

Squeeze

Reynolds Equation


2 2 2

1,2 2 2 2

, ,2, , , ,

2 2

l

l c

P X Y dX dYX Y cH X Y H X Y

r X X Y Y

• Film thickness equation:

• Viscosity & Density Variation with Pressure:

8

0ln 9.67 1 /1.98 10 1z

hp P

P e

9

9

0.59 10 1.34

0.59 10

h

h

p PP

p P

3 3

12 12

H HH P H P

X X Y Y X

Governing Equations

• Reynolds equation:


Finite Difference Discretization

Discretize over a grid, and convert Reynolds Equation to finite difference form:

The Reynolds Equation, in dimensionless form:

3 3

12 12

H HH P H P

X X Y Y X

3 3

3 3

0

1

12 12

1

12 12

E P P W

e w

N P P S

n s

P W

H P P H P P

X X X

H P P H P P

Y Y Y

H H H H

X

EPW

N

S

ΔX

ΔY


Mixed Elastohydrodynamic Lubrication


Surface Deflection

Piezoviscosity

Asperity Contact

Lubricant Flow

Surface

DeformationAsperity Contact

Lubricant Flow

Surface

Deformation


Surface Deflection

Piezoviscosity

Ideal Conditions (perfectly smooth surfaces, or thick lubricant film)

Realistic Conditions (rough surfaces, or thin lubricant film)


Asperity Contact – Stochastic Models

2.5( )cP K E F H

216 2

15K

2 2

1 2

1 2

1

1 1E

E E

2.5

2.5

H

F H z H z dz

Greenwood – Tripp (1971)

• Asperity contact is typically handled using a stochastic model

• Model requires several parameters to be determined

– asperity tip radius

– density of asperities

– variance of asperity heights

– (z) height distribution (typically assumed Gaussian)


Friction Force

dAh

uu

x

phdAF ab

zzxfluidf

20,

The friction force is calculated by summing the contributions from both the fluid shear and the solid contact.

dAPF aspsolidsolidf ,Newtonian

Shear

Pressure

Gradient

Load Balance

dAPdAPW aspz lub

The load balance is calculated by summing the contributions from both the fluid pressure and the asperities in contact.


Interlude:

Frictional Heat Activity


Thermal EHLHeat generation/efficiency analysis


• All surfaces are rough

• Characteristics of the surface roughness height distribution determine the contact behavior

Surface Roughness Modeling


Surface Characterization

Contact Pattern

Fillet Stress Distribution

• Arithmetic Mean (Ra)

• Root Mean Square (Rq)

• Skewness (Rsk)

• Kurtosis (Rku)

1

1 zN

a i

iz

R zN

1/ 2

2

1

1 zN

q i

iz

R zN


Surface CharacterizationThe Autocorrelation Function (ACF) is a measure of how similar the texture is at a given distance from the original location.


Optical Profilometry


Surface CharacterizationBearing Example

Inner Race

Top/row 1

Middle/row 2

Bottom/row 3

Columns 1 2 3

Outer Race

Top/row 1

Middle/row 2

Bottom/row 3

Columns 1 2 3


Surface CharacterizationRaw data

Filtered data

Calculate Statistics, ACFGenerate Surface, Check Statistics


Surface Characterization

Addendum Dedendum Pitch


Deterministic Mixed-EHL Modeling of Drivetrain Components

• The influence of microasperity contact must be taken into account when modeling surface fatigue.

• Sentient’s mixed-EHL solver utilizes real (simulated) surface roughness profiles in an explicit-deterministic calculation of surface tractions– Outcome: We can directly determine the performance of a given surface

finish during the generation, sustainment, and/or failure of an EHL film at the contact zone.

Mixed-EHL pressure profiles for progressively smoother surface roughness (scaled RMS)


Time-dependent Operating Conditions

• Load• Curvature• Surface Velocities• Roughness


Deterministic Mixed-EHL

Ground finish Superfinish

Contact Pressure

Asperity Contacts


Mixed-EHL Modeling of Superfinished Surfaces


Fretting Wear


Fretting Maps

Contact Pattern


250

750

1250

1750

2250

2750

1000 2000 3000 4000 5000 6000

No

rmal

Fo

rce

(lb

f)

Axial Force (lbf)

No

fai

lure

DigitalClone generates the fretting wear map similar to the typical fretting maps.


Microstructure-Based

Fatigue Model


Microstructure Modeling

Contact Pattern


EDM Sectioned

Residual Stress Analysis

Surface Roughness Analysis

Microstructure Analysis

• Spur gear (example) is used for microstructure, micro-hardness, surface roughness and residual stress analysis– Ground finished AISI 8620 steel

• Optical zoom microscopy, scanning electron microscopy (SEM), Inverted microscopy, X-ray diffraction (XRD), optical profilometry, and micro-hardness testing are used for characterization

• Goal is to identify key microstructural features, based on ASM standards


Microstructure Modeling

Contact Pattern


Contact Surface

Subsurface AISI 8620 microstructure

RVE size: 8.42 mm x 0.7 mm

• Thorough evaluation of the microstructure

of the material

• Material microstructure, residual stresses,

surface roughness and material properties are direct inputs to DigitalClone

• Microstructure model input parameters remain the same if the component is made of the same material and manufacturing process


Microstructure-Based Fatigue Model


Calculate Time to Mechanical FailureDetermine Failure Mode &

Account for Model Uncertainty


Calculate Time to Mechanical FailureDetermine Failure Mode

Contact Pattern


Bending Fatigue Fretting Fatigue

Multiple surface initiated cracks on both sides of contact


Putting it all together


System-Level Load AnalysisExample: Wind Turbine Gearbox


Contact Pattern

Macro-stress analysis at the tooth contact provides input to lubrication model

Contact pattern, Contact pressure, Stressed volume, Relative velocity, Curvature

System-Level Load AnalysisDetermine Component Hot Spots

• Build computational models of different components

• Analyze stresses translated from system loads

• Determine high stress regions of component

Contact Pattern


Example: Bearing Supplier Qualification


Bearing CharacterizationGeometry

0

20

40

60

80

100

120

140

0 10000 20000 30000 40000 50000

Bearing 'A'

Bearing 'B'

Bearing 'C'

0

10

20

30

40

50

60

70

80

0 5000 10000 15000 20000 25000 30000 35000

Bearing 'A'

Bearing 'B'

Bearing 'C'

0

5

10

15

20

25

30

0 10000 20000 30000 40000

Bearing 'A'

Bearing 'B'

Bearing 'C'

Outer Race

Inner Race

Roller


higher retained austenite

Bearing ‘A’ Bearing ‘B’ Bearing ‘C’

Bearing CharacterizationMaterial



Contact Surface

Pit/spall location

Contact Surface

Subsurface microstructure3,850 grains

RVE size: 2.84 mm x 0.7 mm

Bearing Fatigue Life PredictionsBearing ‘C’ Inner Race Simulations

• Bearing ‘C’ fatigue life, sample run = 7.79E+06 shaftrevolutions

• Crack initiation location: 75.00 µm in to the depth, Surface pit Size: 120µm

Contact Surface

Subsurface crack networkSurface pit size: 120 m

Bearing Fatigue Life Comparison Bearing ‘A’ vs Bearing ‘C’

Bearing ‘A’

Bearing ‘C’


Summary

• Why modeling is beneficial

• Approaches to modeling EHL/mixed-EHL modeling for gears & bearings

• Approaches to modeling rolling contact fatigue


Supplemental Slides


Derivation of Reynolds Equation (1/4)

Mass flow through rectangular-section control volume: a) x, z plane; b) y, z plane; c) x, y plane

(Hamrock, 1994)



yxqq

hx y t

h

h ht t t

a b a a

h hh w w u v h

t x y t

The mass of lubricant in the control volume at any instant is h x y

Conservation of mass states that the rate of accumulation must be equal to the difference between the mass flux into and out of the control volume

Expand the RHS using chain rule:

Note the rate of change of h, from the CV diagram:



3

0

3

0

12 2

12 2

a bhx

x

h

a by

y

h p u uq hq udz x

h p v vq vdz q hy

Expressions for flow rate can be derived by integration of the reduced Navier-Stokes eqns:

2

2

2

2

u z p A z p zp uu A B

z x xx z z

p v z p zv z p Cv C D

y z z yz y

Assuming zero slip at the fluid-solid interface, the boundary conditions are:

1. 0, ,

2. , ,

b b

a a

z u u v v

z h u u v v

2

2

b a

b a

h z p h z zu z u u

x h h

h z p h z zv z v v

y h h

The flow rates are then found by integrating the velocity across the film



yxa b a a

qq h hw w u v h

x y x y t

3 3

012 12 2

2

a b

a b

a b a a

h u uh p h p

x x y y x

h v v h h pw w u v h

y x y t

Substituting the flow rates into the conservation equation yields the general Reynolds Equation:


Microstructure-Based Fatigue model

Contact Pattern



Microstructure ModelingExample: Coating Microstructure


Rough Surface Stick/Slip Fretting Model

Smooth surface traction and stress analysis

Rough surface traction and stress analysis



Further expanding the LHS with central differencing:

3 3

3 3

0

1

12 12

1

12 12

E P P W

e w

N P P S

n s

P W

H P P H P P

X X X

H P P H P P

Y Y Y

H H H H

X

0

e E P w P W n N P s P S

P W P P

a P P a P P a P P a P P

H H H H

X

3 3

2 2

3 3

2 2 2 2

1 1

12 12

1 1

12 12

e w

e w

n s

n n

H Ha a

X X

H Ha a

Y Y

Grouping terms and simplifying:

where the face coefficients are defined as:



The equation must be modified to include the internal flow disruption boundary condition:

which is used to derive a Neumann type boundary condition for pressure on the east cell face:

3

012 2

a bx e

e

h p u uq h

x

1 2 2

6

e

P

X H

The flowrate for a Newtonian, isothermal fluid is given by:



Thus, flow through the control volume ‘P’ would be described by:

where the source term Bs is used to account for the zero flow boundary condition on the east control volume face

w P W n N P s P S

P W P Ps

a P P a P P a P P

H H H HB

X

2

s

HB

X


63

OEM Test Data

Baseline\OEM

Baseline\OEM

DigitalClone Validation - Taper Roller Bearing OEM


Model Verification with NASA Spur Gear Fatigue Test Data

NASA Data Townsend (1995) TM-107017Townsend (1982) TP-2047Krantz (2004) ASME

Parameter NASA Sentient CLP

Weibull Slope 2.2 2.78

L10 22 27

L50 52 54

L90 89 84


Modeling Tribological Contacts in Wind Turbine Gearboxes

Engineering

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