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Modeling Tribological Contacts
In Wind Turbine Gearboxes
Model-based, multi-physics based
prognostics computational technologies
and services
Our applications help extend the rema...
Our 10 Year Research Pedigree Invited a New way to Measure
and Test Rotating Equipment Computationally
DEPARTMENT
OF DEFEN...
Sentient Science Services
Fundamental Capabilities
• Highly accurate reliability and performance predictions
• Holistic ap...
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Computational Testing Customer Base
World’s Most Tested Products
Webinar: Modeling Tribological Contacts in Wind Turbine G...
DigitalClone Live Customer Base
Products with the Lowest Cost of Operation
Webinar: Modeling Tribological Contacts in Wind...
Why do we model?
• Physical testing is expensive and time consuming
• Physics-based models give us insight into the perfor...
What is Tribology?
• The science and engineering of interacting surfaces in
relative motion.
• The study and application o...
Figure 1: Spall propagation for a cylindrical roller bearing (SKF NU1012ML) under radial loading.
Rolling direction is rig...
Stribeck Curve
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Elastohydrodynamic Lubrication
Lubricant
Pressurization
Surface
Deflection
Piezoviscosity
LubricantFlow
Surface
Deformatio...
Lubrication Assumptions
xF
z
u
y
u
x
u
x
p
z
u
w
y
u
v
x
u
u
t
u
 






















...
     
221212
33
t
h
y
h
v
x
h
uww
vvh
y
uuh
xy
ph
yx
ph
x
aaba
baba













 







...
     
 
   
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

   
 
  ...
Finite Difference Discretization
Discretize over a grid, and convert
Reynolds Equation to finite difference form:
The Reyn...
Mixed Elastohydrodynamic Lubrication
Lubricant
Pressurization
Surface
Deflection
Piezoviscosity
Asperity
Contact
Lubricant...
Mixed Elastohydrodynamic Lubrication
Lubricant
Pressurization
Surface
Deflection
Piezoviscosity
Asperity
Contact
Lubricant...
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
 
 
 ...
Friction Force
    dA
h
uu
x
ph
dAF ab
zzxfluidf  
 




 






20,
The friction force is calcu...
Interlude:
Frictional Heat Activity
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Thermal EHL
Heat generation/efficiency analysis
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
• All surfaces are rough
• Characteristics of the surface roughness height
distribution determine the contact behavior
Sur...
Surface Characterization
Contact
Pattern
Fillet Stress
Distribution
• Arithmetic Mean (Ra)
• Root Mean Square (Rq)
• Skewn...
Surface Characterization
The Autocorrelation Function (ACF) is a measure of
how similar the texture is at a given distance...
Optical Profilometry
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Surface Characterization
Bearing Example
Inner Race
Top/row 1
Middle/row 2
Bottom/row 3
Columns 1 2 3
Outer Race
Top/row 1...
Surface CharacterizationRaw data
Filtered data
Calculate Statistics, ACF
Generate Surface, Check Statistics
Webinar: Model...
Surface Characterization
Addendum Dedendum Pitch
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Deterministic Mixed-EHL Modeling of
Drivetrain Components
• The influence of microasperity contact must be taken into acco...
Time-dependent Operating Conditions
• Load
• Curvature
• Surface Velocities
• Roughness
Webinar: Modeling Tribological Con...
Deterministic Mixed-EHL
Ground finish Superfinish
Contact Pressure
Asperity Contacts
Webinar: Modeling Tribological Contac...
Mixed-EHL Modeling of Superfinished Surfaces
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Fretting Wear
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Fretting Maps
Contact
Pattern
Fillet Stress
Distribution
250
750
1250
1750
2250
2750
1000 2000 3000 4000 5000 6000
NormalF...
Microstructure-Based
Fatigue Model
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Microstructure Modeling
Contact
Pattern
Fillet Stress
Distribution
EDM
Sectioned
Residual Stress
Analysis
Surface Roughnes...
Microstructure Modeling
Contact
Pattern
Fillet Stress
Distribution
Contact Surface
Subsurface AISI 8620
microstructure
RVE...
Microstructure-Based Fatigue Model
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Microstructure-Based Fatigue Model
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Calculate Time to Mechanical Failure
Determine Failure Mode &
Account for Model Uncertainty
Webinar: Modeling Tribological...
Calculate Time to Mechanical Failure
Determine Failure Mode
Contact
Pattern
Fillet Stress
Distribution
Bending Fatigue Fre...
Putting it all together
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
System-Level Load Analysis
Example: Wind Turbine Gearbox
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes...
Contact
Pattern
 Macro-stress analysis at the tooth contact
provides input to lubrication model
 Contact pattern, Contac...
Example: Bearing Supplier Qualification
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Bearing Characterization
Geometry
0
20
40
60
80
100
120
140
0 10000 20000 30000 40000 50000
Bearing 'A'
Bearing 'B'
Bearin...
higher retained austenite
Bearing ‘A’ Bearing ‘B’ Bearing ‘C’
Bearing Characterization
Material
Webinar: Modeling Tribolog...
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Contact Surface
Pit/spall location
Contact Surfa...
Bearing Fatigue Life Comparison
Bearing ‘A’ vs Bearing ‘C’
Bearing ‘A’
Bearing ‘C’
Webinar: Modeling Tribological Contacts...
Summary
• Why modeling is beneficial
• Approaches to modeling EHL/mixed-EHL
modeling for gears & bearings
• Approaches to ...
Supplemental Slides
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
1/28/15
Derivation of Reynolds Equation (1/4)
Mass flow through rectangular-
section control volume: a) x, z
plane; b) y, z plane;...
Derivation of Reynolds Equation (2/4)
 yx
qq
h
x y t


 
  
  
 
h
h h
t t t

 
  
 
  
  a...
Derivation of Reynolds Equation (3/4)
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


 
...
Derivation of Reynolds Equation (4/4)
yx
a b a a
qq h h
w w u v h
x y x y t
 

     
           ...
Microstructure-Based Fatigue model
Contact
Pattern
Fillet Stress
Distribution
Webinar: Modeling Tribological Contacts in W...
Microstructure Modeling
Example: Coating Microstructure
Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes
...
Rough Surface Stick/Slip Fretting Model
Smooth surface
traction and stress
analysis
Rough surface
traction and stress
anal...
Finite Difference Discretization
Further expanding the LHS with
central differencing:
       
3 3
3 3
0
1
12 12
1
...
Finite Difference Discretization
The equation must be modified to include the
internal flow disruption boundary condition:...
Finite Difference Discretization
Thus, flow through the control volume ‘P’ would
be described by:
where the source term Bs...
63
OEM Test Data
BaselineOEM
BaselineOEM
DigitalClone Validation - Taper Roller Bearing OEM
Webinar: Modeling Tribological...
Model Verification with NASA Spur Gear Fatigue Test Data
NASA Data
Townsend (1995) TM-107017
Townsend (1982) TP-2047
Krant...
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Modeling Tribological Contacts in Wind Turbine Gearboxes

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Sentient Science outlines how we build a multi-physics solver for rolling contact and fatigue modeling that predicts where both long and short crack nucleate and initiate before system failure occurs.

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Modeling Tribological Contacts in Wind Turbine Gearboxes

  1. 1. Modeling Tribological Contacts In Wind Turbine Gearboxes
  2. 2. Model-based, multi-physics based prognostics computational technologies and services Our applications help extend the remaining useful life (RUL) of new and existing mechanical systems The newest prognostics health management (PHM) application for condition-based maintenance (CBM) Sentient Science is Based on Three Fundamental Capabilities Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  3. 3. Our 10 Year Research Pedigree Invited a New way to Measure and Test Rotating Equipment Computationally DEPARTMENT OF DEFENSE DEPARTMENT OF ENERGY NATIONAL SCIENCE FOUNDATION Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  4. 4. 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 Predict impact of feature level design factors on component performance Complete solution for optimal lifecycle management of fielded assets Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  5. 5. Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  6. 6. Computational Testing Customer Base World’s Most Tested Products Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  7. 7. DigitalClone Live Customer Base Products with the Lowest Cost of Operation Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  8. 8. 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  9. 9. 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  10. 10. 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  11. 11. Stribeck Curve Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  12. 12. Elastohydrodynamic Lubrication Lubricant Pressurization Surface Deflection Piezoviscosity LubricantFlow Surface Deformation Science Applications Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  13. 13. 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  14. 14.       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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  15. 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: Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  16. 16. 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  17. 17. 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) Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  18. 18. 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) Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  19. 19. 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) Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  20. 20. 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. Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  21. 21. Interlude: Frictional Heat Activity Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  22. 22. Thermal EHL Heat generation/efficiency analysis Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  23. 23. • All surfaces are rough • Characteristics of the surface roughness height distribution determine the contact behavior Surface Roughness Modeling Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  24. 24. 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          Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  25. 25. Surface Characterization The Autocorrelation Function (ACF) is a measure of how similar the texture is at a given distance from the original location. Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  26. 26. Optical Profilometry Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  27. 27. Surface Characterization 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  28. 28. Surface CharacterizationRaw data Filtered data Calculate Statistics, ACF Generate Surface, Check Statistics Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  29. 29. Surface Characterization Addendum Dedendum Pitch Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  30. 30. 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) Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  31. 31. Time-dependent Operating Conditions • Load • Curvature • Surface Velocities • Roughness Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  32. 32. Deterministic Mixed-EHL Ground finish Superfinish Contact Pressure Asperity Contacts Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  33. 33. Mixed-EHL Modeling of Superfinished Surfaces Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  34. 34. Fretting Wear Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  35. 35. 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. Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  36. 36. Microstructure-Based Fatigue Model Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  37. 37. 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  38. 38. Microstructure Modeling 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  39. 39. Microstructure-Based Fatigue Model Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  40. 40. Microstructure-Based Fatigue Model Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  41. 41. Calculate Time to Mechanical Failure Determine Failure Mode & Account for Model Uncertainty Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  42. 42. 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  43. 43. Putting it all together Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  44. 44. System-Level Load Analysis Example: Wind Turbine Gearbox Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  45. 45. 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  46. 46. Example: Bearing Supplier Qualification Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  47. 47. 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  48. 48. higher retained austenite Bearing ‘A’ Bearing ‘B’ Bearing ‘C’ Bearing Characterization Material Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  49. 49. Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 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
  50. 50. Bearing Fatigue Life Comparison Bearing ‘A’ vs Bearing ‘C’ Bearing ‘A’ Bearing ‘C’ Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  51. 51. Summary • Why modeling is beneficial • Approaches to modeling EHL/mixed-EHL modeling for gears & bearings • Approaches to modeling rolling contact fatigue Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  52. 52. Supplemental Slides Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  53. 53. 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) Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  54. 54. Derivation of Reynolds Equation (2/4)  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: Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  55. 55. Derivation of Reynolds Equation (3/4) 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  56. 56. Derivation of Reynolds Equation (4/4) 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: Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  57. 57. Microstructure-Based Fatigue model Contact Pattern Fillet Stress Distribution Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  58. 58. Microstructure Modeling Example: Coating Microstructure Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  59. 59. Rough Surface Stick/Slip Fretting Model Smooth surface traction and stress analysis Rough surface traction and stress analysis Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  60. 60. Finite Difference Discretization 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: Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  61. 61. Finite Difference Discretization 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: Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  62. 62. Finite Difference Discretization 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     Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  63. 63. 63 OEM Test Data BaselineOEM BaselineOEM DigitalClone Validation - Taper Roller Bearing OEM Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15
  64. 64. 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 Webinar: Modeling Tribological Contacts in Wind Turbine Gearboxes 1/28/15

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