reduction of teeter angle excursions for a two-bladed downwind rotor using cyclic pitch control...
TRANSCRIPT
![Page 1: REDUCTION OF TEETER ANGLE EXCURSIONS FOR A TWO-BLADED DOWNWIND ROTOR USING CYCLIC PITCH CONTROL Torben Juul Larsen, Helge Aagaard Madsen, Kenneth Thomsen,](https://reader035.vdocuments.net/reader035/viewer/2022062804/56649efd5503460f94c110c0/html5/thumbnails/1.jpg)
REDUCTION OF TEETER ANGLE EXCURSIONS FOR A TWO-BLADED DOWNWIND ROTOR
USING CYCLIC PITCH CONTROL
Torben Juul Larsen,
Helge Aagaard Madsen,
Kenneth Thomsen,
Flemming Rasmussen
Risø, National Laboratory
Technical University of Denmark
EWEC 2007,7.-10. May, Milano
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Outline
• The 2-bladed turbine
• The simulation platform – HAWC2
• The teeter mechanism
• 3 influence
• The cyclic pitch control
• The control alternative – teeter velocity proportional control - and the combination
• Results
• Conclusion
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The 2-bladed turbine
• Data based on 3-bladed fictive turbine used in IEA annex 23 benchmark.
• 3 blades replaced by 2 with same radius and solidity.
• Downwind configuration. Tilt angle included – no cone angle.
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Scaling laws for blade scaling
• Aerodynamic layout:•Radius constant 61.5 m
•Chord and height x 1.5 (constant solidity)
• Structural layout scale parameters•Constant material stress
•Aerodynamic loads
• Structural layout - results
•The material thickness
•Cross sectional area – and mass
•Bending stiffness
•Torsion stiffness
BB 23 BB LL 32 5.1
BB tt 32 667.0
BB AA 32
BB II 32 2.2BB KK 32 5.1
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The simulation platform HAWC2
• Structural model based on a multibody formulation. The turbine structure is modeled as a number of bodies interconnected by joints.
• Each body include its own coordinate system, hence large rotations are accounted for by a proper subdivision of bodies.
• Within a body small deflections and
rotations are assumed.
• Forces are placed on the structure
in the deflected state, which is
essential for pitch loads of
the blades.
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The simulation platform HAWC2
• The aerodynamic model is based on Blade Element Momentum. Extended to handle dynamic inflow, dynamic stall, skew inflow, shear effects on the induction and effects of large deflections.
• For downwind turbines a jet model for the tower shadow deficit is used. This deficit changes location according to the turbulence.
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The teeter bearing
• A special bearing that allows for flapwise rotation of the rotor.
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The delta 3 angle
• An angle of the teeter bearing axis that enables a direct coupling between teeter and pitch
))sin()3(arcsin(sin teeter With this defintion of the teeter angle, the change in pitch related to teeter angle is:
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Gyroscopic motion
Basic knowledge of gyroscopic motion is essential for the understanding of two-bladed teetering rotors.
A disc spinning with constant speed will turn 90° after the load impact.
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The basic teeter motion
The teeter motion can traditionally be seen in two ways
1. From the shaft in a rotating frame of reference. (classical approach)
• The centrifugal force is a stiffness term of teeter motion.
• It can be shown that this system has an eigenfrequency of 1P.
• A delta 3 coupling will change this natural frequency – but does it reduce the teeter angles?
• Aerodynamic forces change the damping of the system.
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Basic teeter motion - continued
2. From outside in a fixed frame of reference. The rotor spins in a plane not perpendicular to the shaft. In this plane a kind of cyclic pitch occurs. This cyclic pitch has a maximum at 90 degrees before the teeter maximum.
Another way of observing the system:
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Basic teeter motion – linear shear case
Special linear shear at 8m/s. 16m/s in top, 0m/s in bottom
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Delta 3 coupling – example 8m/s
Special linear shear at 8m/s. 16m/s in top, 0m/s in bottom
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Delta 3 coupling – example 20m/s
Special linear shear at 8m/s. 16m/s in top, 0m/s in bottom
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Finding the teeter plane- decoupled around two axes
cos
sin
teeterTz
teeterTx
teeter
Front view Side view
z
x
z
y
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A PI-regulator on each axis is aplied
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1 )cos()sin(Bcyc
Bcyc
pitchz
pitchx
Bcyc
And the phase shift of β=90° is included in the transformation to pitch angles. Servo delays can also be included in this angle
PI0
pitchxT
x
PIpitchzT
z
0
z
x
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Filters need to be included too
cos
sin
teeterTz
teeterTx
Tz
Tx
PI0
pitchxfiltT
x,
teeter
Tz
PIpitchzfiltT
z,
2P 1P
0
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Cyclic pitch example – linear shear case
Special linear shear at 8m/s. 16m/s in top, 0m/s in bottom
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Alternative control using teeter velocity proportional pitch
12
1
Bcyc
Bcyc
teetergainBcyc k
Special linear shear at 8m/s. 16m/s in top, 0m/s in bottom
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Different qualities for the approaches. 20m/s with turbulence
Collective pitch: A large deterministic 1P content present.
Cyclic pitch: The determistic 1P content removed.
Velocity proportional pitch: General load reduction, but 1P content still present.
The combination of cyclic and velocity proportional pitch joins the advantages.
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Operational loads 4-25m/s – statistics – IEA61400 class IA
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Operational loads 4-25m/s - statistics
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Operational loads – 20 years of operation
m Col Cyc Vel Cyc+Vel
Blade 1 flap 12 1.00 1.00 1.01 1.01
Blade 1 edge 12 1.00 1.01 1.01 1.02
Blade 1 torsion 8 1.00 0.99 0.99 1.00
Tower top tilt 5 1.00 1.01 1.01 1.01
Tower top side 5 1.00 0.98 1.00 0.99
Tower top yaw 5 1.00 1.00 1.00 1.00
Tower bottom tilt 5 1.00 0.99 1.00 0.99
Tower bottom side 5 1.00 0.97 0.97 0.97
Tower bottom yaw 5 1.00 1.00 1.00 1.00
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Conclusion
• Cyclic pitch can be used to limit teeter excursions without causing extra loads
• If a direct coupling between teeter velocity and blade pitch can be done this is a very simple and efficient way to limit teeter excursions.
• A coupling between cyclic pitch and velocity proportional pitch is possible and gives very good result. A reduction of 52% teeter angle excursion is possible – IEC 61400-1 class IA operational loads.
• Delta 3 coupling in the teeter bearing does not reduce teeter angle excursion (for this size of turbine) but induce extra loads. This does not seem to be a a good approach for a modern large scale turbine!