Modeling Tribological Contacts in Wind Turbine Gearboxes Webinar

Modeling Tribological Contacts
In Wind Turbine Gearboxes

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Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15

Our 10 Year Research Pedigree Invited a New way to Measure
and Test Rotating Equipment Computationally
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Sentient Science Services
Fundamental 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
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component performance
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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
1/28/15

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 Bearing
Gearbox Gears
and Bearings
Yaw Gear
1/28/15

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
Background
Contact Fatigue
1/28/15

Stribeck Curve
1/28/15

Elastohydrodynamic Lubrication
Lubricant
Pressurization
Surface
Deflection
Piezoviscosity
LubricantFlow
Surface
Deformation
Science Applications
1/28/15

Lubrication Assumptions
xF
z
u
y
u
x
u
x
p
z
u
w
y
u
v
x
u
u
t
u
 

































2
2
2
2
2
2
yF
z
v
y
v
x
v
y
p
z
v
w
y
v
v
x
v
u
t
v
 

































2
2
2
2
2
2
zF
z
w
y
w
x
w
z
p
z
w
w
y
w
v
x
w
u
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
1/28/15

     
221212
33
t
h
y
h
v
x
h
uww
vvh
y
uuh
xy
ph
yx
ph
x
aaba
baba













 







 





















 






     
WedgePhysicalStretchdgeDensity We
222 x
huu
uu
x
h
x
uuh ba
ba
ba







 
Poiseuille:
Flow
Direction
Poiseuille:
Cross-Flow
Direction
Couette:
Flow
Direction
Couette:
Cross-Flow
Direction
Normal
Squeeze
Local
Expansion
Translational
Squeeze
Reynolds Equation
1/28/15

     
 
   
2 2 2
1,2 2 2 2
, ,2
, , , ,
2 2
l
l c
P X Y dX dYX Y c
H 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 1
z
hp P
P e


        
  
9
9
0.59 10 1.34
0.59 10
h
h
p P
P
p P

 

 
   3 3
12 12
H HH P H P
X X Y Y X
  
 
  
       
     
        
Governing Equations
• Reynolds equation:
1/28/15

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
1/28/15

Mixed Elastohydrodynamic Lubrication
Lubricant
Pressurization
Surface
Deflection
Piezoviscosity
Asperity
Contact
Lubricant Flow
Surface
DeformationAsperity Contact
Lubricant Flow
Surface
Deformation
Lubricant
Pressurization
Surface
Deflection
Piezoviscosity
Ideal Conditions (perfectly smooth surfaces, or thick lubricant film)
Realistic Conditions (rough surfaces, or thin lubricant film)
1/28/15

Asperity Contact – Stochastic Models
2.5( )cP K E F H 
 
216 2
15
K
 


 
2 2
1 2
1 2
1
1 1
E
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)
1/28/15

Friction Force
    dA
h
uu
x
ph
dAF 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.
1/28/15

Interlude:
Frictional Heat Activity
1/28/15

Thermal EHL
Heat generation/efficiency analysis
1/28/15

• All surfaces are rough
• Characteristics of the surface roughness height
distribution determine the contact behavior
Surface Roughness Modeling
1/28/15

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 z
N 
 
1/2
2
1
1 zN
q i
iz
R z
N 
 
  
 

1/28/15

The Autocorrelation Function (ACF) is a measure of
how similar the texture is at a given distance from
the original location.
1/28/15

Optical Profilometry
1/28/15

Bearing 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
1/28/15

Surface CharacterizationRaw data
Filtered data
Calculate Statistics, ACF
Generate Surface, Check Statistics
1/28/15

Addendum Dedendum Pitch
1/28/15

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)
1/28/15

Time-dependent Operating Conditions
• Load
• Curvature
• Surface Velocities
• Roughness
1/28/15

Deterministic Mixed-EHL
Ground finish Superfinish
Contact Pressure
Asperity Contacts
1/28/15

Mixed-EHL Modeling of Superfinished Surfaces
1/28/15

Fretting Wear
1/28/15

Fretting Maps
Contact
Pattern
Fillet Stress
Distribution
250
750
1250
1750
2250
2750
1000 2000 3000 4000 5000 6000
NormalForce(lbf)
Axial Force (lbf)
Nofailure
DigitalClone generates the fretting wear map similar to the typical fretting maps.
1/28/15

Microstructure-Based
Fatigue Model
1/28/15

Microstructure Modeling
Contact
Pattern
Fillet Stress
Distribution
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
1/28/15

Contact
Pattern
Fillet Stress
Distribution
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
1/28/15

Microstructure-Based Fatigue Model
1/28/15

Calculate Time to Mechanical Failure
Determine Failure Mode &
Account for Model Uncertainty
1/28/15

Calculate Time to Mechanical Failure
Determine Failure Mode
Contact
Pattern
Fillet Stress
Distribution
Bending Fatigue Fretting Fatigue
Multiple surface initiated cracks on
both sides of contact
1/28/15

Putting it all together
1/28/15

System-Level Load Analysis
Example: Wind Turbine Gearbox
1/28/15

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 Analysis
Determine Component Hot Spots
• Build computational models of
different components
• Analyze stresses translated from
system loads
• Determine high stress regions of
component
Contact
Pattern
1/28/15

Example: Bearing Supplier Qualification
1/28/15

Bearing Characterization
Geometry
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
1/28/15

higher retained austenite
Bearing ‘A’ Bearing ‘B’ Bearing ‘C’
Bearing Characterization
Material
1/28/15

1/28/15
Contact Surface
Pit/spall location
Contact Surface
Subsurface
microstructure
3,850 grains
RVE size: 2.84 mm x 0.7 mm
Bearing Fatigue Life Predictions
Bearing ‘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 network
Surface pit size: 120 m

Bearing Fatigue Life Comparison
Bearing ‘A’ vs Bearing ‘C’
Bearing ‘A’
Bearing ‘C’
1/28/15

Summary
• Why modeling is beneficial
• Approaches to modeling EHL/mixed-EHL
modeling for gears & bearings
• Approaches to modeling rolling contact
fatigue
1/28/15

Supplemental Slides
1/28/15

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)
1/28/15

 yx
qq
h
x y t


 
  
  
 
h
h h
t t t

 
  
 
  
  a b a a
h h
h 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:
1/28/15

3
0
3
0
12 2
12 2
a bh
x
x
h
a b
y
y
h p u u
q hq udz x
h p v vq vdz q h
y


 
     

      



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 u
u A B
z x xx z z
p v z p zv z p C
v 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 z
u z u u
x h h
h z p h z z
v z v v
y h h


   
      
   
      
The flow rates are then found by integrating the velocity across the film
1/28/15

yx
a b a a
qq h h
w w u v h
x y x y t
 

     
            
 
 
 
3 3
0
12 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 p
w w u v h
y x y t
 
 

  
        
                  
    
          
Substituting the flow rates into the conservation equation yields the general Reynolds Equation:
1/28/15

Microstructure-Based Fatigue model
Contact
Pattern
Fillet Stress
Distribution
1/28/15

Example: Coating Microstructure
1/28/15

Rough Surface Stick/Slip Fretting Model
Smooth surface
traction and stress
analysis
Rough surface
traction and stress
analysis
1/28/15

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 H
a a
X X
H H
a a
Y Y
 
 
 
   
   
        
   
        
Grouping terms and simplifying:
where the face coefficients are defined as:
1/28/15

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
0
12 2
a b
x e
e
h p u u
q h
x
   
     
 1 2 2
6
e
P
X H

 
  
   
  
The flowrate for a Newtonian, isothermal fluid is given by:
1/28/15

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 P
s
a P P a P P a P P
H H H H
B
X
   
 


      
 
 
 
 
2
s
H
B
X
 


1/28/15

63
OEM Test Data
BaselineOEM
BaselineOEM
DigitalClone Validation - Taper Roller Bearing OEM
1/28/15

Model Verification with NASA Spur Gear Fatigue Test Data
NASA Data
Townsend (1995) TM-107017
Townsend (1982) TP-2047
Krantz (2004) ASME
Parameter NASA Sentient CLP
Weibull Slope 2.2 2.78
L10 22 27
L50 52 54
L90 89 84
1/28/15

Modeling Tribological Contacts in Wind Turbine Gearboxes Webinar

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