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

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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!