Understanding the Life of Power Transmission Elements of Wind
Turbine Systems
Understanding the Life of Power Transmission Elements of Wind
Turbine Systems
Jian Cao and Q. Jane Wang
Northwestern University
March 2010
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Northwestern UniversityNorthwestern University
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Wind Resource Assessment
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Great ChallengesGreat ChallengesAdvanced product design requirements impose great challenges:
high power density high efficiency high reliabilityextreme conditions
e.g. Windmill gearboxes:Power up to 5-10 MW, going to 15 MWunbalanced/unstable loadingvery long operating durationextreme weather conditionsminimal maintenance.
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Counterformal Contact in GearsCounterformal Contact in Gears
Typical line contact during a meshing cycle in helical/ spur/worm/straight bevel gears
From A. Erdemir
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Ra=698.8 nm, Rq=886.4 nm, Rt=18430 nm Ra=512.6 nm, Rq=657.0 nm, Rt=10720 nm
Ra=270.5 nm, Rq=346.3 nm, Rt=7200 nm Ra=189.2 nm, Rq=280.2 nm, Rt=5430 nm
Shaved Ground
Honed Polished
Surface roughness is usually of the same order of magnitude as, or greater than, the possible EHL (elasto-hydrodynamic lubrication) film thicknessSurface topography is 3-dimensional, although macro contact geometry may be simplified to 2-dimensional.
A 3-dimensional mixed EHL model capable of handing real machined roughness is needed even for line contact problems
Gear as an ExampleGear as an Example
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3-D Line Contact Mixed EHL Model3-D Line Contact Mixed EHL ModelThe Reynolds Equation:
Film Thickness Equation:
Surface Deformation:
Load Equation:
Lubricant Viscosity Model:
( ) ( , , )pW t p x y t dxdyΩ
= ∫∫
0peαη η=
2
0 1 2( ) ( , , ) ( , , ) ( , , )2 x
xh h t v x y t x y t x y tR
δ δ= + + + +
3 3 ( ) ( )12 12
p p h hh h Ux x y y x t∂ ρ ∂ ∂ ρ ∂ ∂ ρ ∂ ρ∂ η ∂ ∂ η ∂ ∂ ∂
⎛ ⎞⎛ ⎞+ = +⎜ ⎟⎜ ⎟
⎝ ⎠ ⎝ ⎠
2 2
2 ( , , )( , , )' ( ) ( )
p tv x y t d dE x y
ξ ς ξ ςπ ξ ςΩ
=− + −
∫∫
Based on the mixed EHL model by Zhu & Hu (1999-2000) for point contacts, and contact model with mixed FFT approach by W. Chen & Q. Wang (2007)
Ren et al., J. Tribology, 2009Chen, W. W., Wang, Q., Wang, F., Keer, L. M., and Cao, J. J. Applied Mechanics (2008)
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Line Contact Mixed EHL SolutionLine Contact Mixed EHL Solution
Film Thickness or Gap PressureTwo shaved cylindrical surfaces running against each other at a rolling speed of 500 mm/s and a slide-to-roll ratio of 25%. Max. Hertzian pressure 1.883 GPa
Both hydrodynamic lubrication and surface asperity contacts are simulated with a unified equation system and numerical approach.
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Typical Mixed EHL SolutionsTypical Mixed EHL SolutionsFor a spur gear set under LPSTC conditions, PH =2.919 GPa, SR=114.3%
From Zhu et al., J. Tribology, 2009
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Friction in GearsFriction in GearsTooth contact friction is often the single largest source of power loss in a gearboxTotal friction is the sum of hydrodynamic friction and asperity contact frictionFriction can be predicted based on the mixed lubrication analysis
In hydrodynamic areas:using Bair & Winer’snon-Newtonian elastic-viscous fluid model:
⎟⎟⎠
⎞⎜⎜⎝
⎛−−=
L
L
xG ττ
ηττγ 1ln
..
In contact areas: using an experimentally estimated boundary lubrication coefficient of friction(Typically 0.08 ~ 0.12). -1.5 -1.0 -0.5 0.0 0.5 1.0
Contact Area
HydrodynamicallyLubricated Area
Pressure
Lubricant FilmThickness
SubsurfaceStress Field
0.07 ~ 0.15 ).Contact friction is usually dominant
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Friction Reduction StrategyFriction Reduction Strategy
(1) Reduce contact friction coefficient (2) Reduce asperity contact (3) Reduce hydrodynamic friction
Mixedlubrication
Boundarylubrication
Full-film (Elastohydrodynamic orhydrodynamic) Lubrication
By low friction materials, coatings,and lubricant additives
Fric
tion
coef
ficie
nt
Lubricant Film Thickness (λ) Ratio
Actual Operating Point
1
2
3
1
23 By improved lubrication techniques,
lubricants, and surface textures
By optimization of design, operatingconditions, and surface finish
Improved Friction Curve
Rougher SurfacesSmoother Surfaces
1
2Current Status
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Effect of Surface FinishEffect of Surface FinishSurface roughness and its orientation greatly affect the lubrication performance and friction. In most cases the smoother the better
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Possible Friction Reduction in GearsPossible Friction Reduction in Gears
From A. Martini, D. Zhu, and Q. Wang, 2007.
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Stress Based Fatigue Life ModelsStress Based Fatigue Life ModelsIoannides-Harris Model (1985):
Zaretsky life model (1987):
8 S - probability of survival (e.g. 50%)8 N - number of stress cycles until initiation8 V - stressed volume8 τe - effective stress (based on
calculated 3D stress)8 z - depth below the surface8 τu, e, c, etc - materials-related constants
∫∫∫V
ece
e dVNS
τ~1ln
∫∫∫−
V
cuee dV
zN
S)(~1ln ττ
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Comparison between Predicted Pitting Life and Test ResultsComparison between Predicted Pitting Life and Test Results
From Zhu, Ren and Wang, 2009
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Surface Finish Effect on Pitting LifeSurface Finish Effect on Pitting Life
From Zhu, Ren and Wang, 2009
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Opportunities and ChallengesOpportunities and Challenges
Opportunities: Recent advancement in contact and lubrication research has provided powerful tools for friction/efficiency and life/durability analysesChallenges:
Market and technology development constantly imposes new challenges (higher power, higher efficiency, better reliability,more compact sizes, lower costs, etc.)There is still a gap between fundamental research and industrial applications
Simulation-based analyses integrated in design for surface strength and friction/efficiency is far behind that for structure strength with FEA
20/22National Renewable Energy Laboratory – M. Robinson
Offshore COE Cost Breakdown
LRC & Lease Cost6%
Electrical Infrastructure
12%
Eng/Permits 4%
Support Structure14%
Misc BOS13%
Offshore Warranty
6%
Turbine32%
O&M (After Tax)13%• Gearbox performance
• Operating expenses to high• Capital expenses still exceed DOE
performance goals• Rotor stretching strategy• Wind plants under-performing 10%
Why:• Bearing failures; inaccurate
internal loads?• Unscheduled maintenance, low
reliability, lack O&M automation• Fatigue load & deflection control
required• Tower clearance limit, materials,
aeroacoustics limiting tip speed, dynamic stability?
Technology Challenges
Onshore COE Cost BreakdownO&M (After Tax)
9%LRC & Lease
Cost10%
Electrical Infrastructure
7%Foundation
3% Misc BOS11%
Turbine60%
Existing design codes & tools should achieve 20 year life & reliable power performance predictions;
What are we missing?
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Future TrendsFuture TrendsSimulation-based tribological analyses, efficiency and surface failure predictions will be integrated in design packages. More precise machining, better surface finish and other surface enhancement techniques (such as coatings) will be widely used especially for critical heavy-duty gears.Advanced lubricant/additive/coating interfacial system design will be developed, significantly improving performance, efficiency and life. New material development is needed.
THANK [email protected]
www.mech.northwestern.edu/fac/caogoogle “Jian Cao”
THANK YOUTHANK [email protected]@northwestern.edu
www.mech.northwestern.edu/fac/caowww.mech.northwestern.edu/fac/caogoogle google ““Jian CaoJian Cao””
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Growth of Wind Energy Capacity WorldwideGrowth of Wind Energy Capacity Worldwide
EUUS
AsiaRest of the World
Pacific
National Renewable Energy Laboratory
010,00020,00030,00040,00050,00060,00070,00080,00090,000
100,000110,000120,000
'00 '01 '02 '03 '04 '05 '06 '07 '08 '09 '10 11 12
MW
Inst
alle
d
Sources: BTM World Market Update 2007; AWEA, January 2009; Windpower Monthly, January 2009
Pacific
Actual Projected
Pacific
Rest of the World Rest of the World
Asia Asia
North America North America
Europe Europe
Jan 2009 Cumulative MW = 115,016
Rest of World = 23,711
North America = 27,416 MWU.S 25,170
Canada 2,246
Europe = 63,889 MW
