Vibrations in wind turbines

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Vibrations in wind turbines

• Vestas Wind Systems A/S

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Agenda

• Linear SDOF systems
• Effects of input forces
• Linear MDOF systems
• Example on effects
• Continuous systems / boundary conditions
• Torsional vibrations
• Wind turbine drive trains
• Rotor disk modelling
• Practical use / real problems
• The presentation is thought as an appetizer, and
  will not cover formulas and development of theory

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Vibrations

• Vibrations is cyclic movements of points on a
  structure
• Complex representation makes mathematical
  handling easier
• Out of phase part represents the amount of
  damping in a structure.
• The movements can be forced or free.
• Frequency is measured in Hz cycles/sec, or
  often angular velocity.

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Damping

• Theoretically structures can be shown without
  damping.
• Real structures will always be more or less
  damped.
• Damping is Energy loss
• Undamped structures will move forever.
• Damped vibrations will die out after some time.
• Typical damping for metallic structures is a
  damping ratio of 0.01
• Typical rubber damping is 0.1 to 0.2.
• Bolted structures can be anything depending on
  friction or other energy losses

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Linear SDOF system

• Developing the differential equations show one
  specific eigenvalue for the system.
• Eigenvalues show up as a peaks in frequency
  response plots.
• Response on input force depend upon frequency.
• Operation below 1.4 times eigenvalue causes
  amplification of forces.
• Operation above reduces forces

f00.4, f01.01, f01.6
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Linear MDOF systems

• If more than one sprint/damper/mass is present in
  a system, we are talking of MDOF systems
• The result are a more complex response, where
  some frequencies are amplified, and some are
  reduced.

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Continous systems / beams
Free-Free                                       
                                                  
                                   
                         Clamped-Clamped
(Fixed-Fixed)                                   
                                                  
                                       
                         Simply Supported at
Both Ends                                       
                                                  
                                   
                         Clamped-Free
(Cantilever Beam)                               
                                                  
                                           
                        
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Torsional vibrations

• Like linear system, rotational systems have
  resonances.
• Behaviour of torsional vibrations is identical
  with linear systems, but more complex to get the
  feeling of.
• Combinations of linear and torsional systems is
  common in the modelling of any system.

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Wind turbine drive train

• A turbine drive train is a combination of 3 beams
  and some rotational elements.
• Blade (beam) bending induces torque on the
  rotational DOFs
• Using traditional tools like VTS regards the
  drive train as two DOFs one at each end.
• Different rpm must be corrected for before
  solving any equations
• Taking a more detailed approach includes at
  minimum modelling of each stage inside the
  gearbox, and brake disk and coupling outside the
  gearbox.
• Detailed modelling needs to take rpm for each
  component into account.

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Rotor disk modelling

• Simple modelling regards the drive train as two
  rotating DOFs.
• Medium advanced step in modelling is rotor disk
  modelling with several DOFs.
• This can have as many elements as desired
  extreme one for each wheel in the drive train.
• State of the art modelling is MBS, where each
  element is given 6 DOF, and any nonlinearities
  between elements is taken into account.

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Practical use

• When force is given in at frequencies close to
  resonances in the turbine, oscillations will
  build up.
• Rule of thumb
• 0 to 10 Hz results in failures within short time
• 10 to 100 Hz results in long term fatigue
• gt 100 Hz results in audible noise.
• Exciting forces can be wind, waves, P, 3P,
  gearbox tooth meshes

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Failure mechanisms

• VTS takes frequencies below 10 Hz into account.
  Good agreement between measured and simulated
  loads are seen.
• Frequencies 10 to 100 Hz, may influence bearing
  and tooth failures. Research is being made for
  clarification of this.
• Frequencies above 100 Hz are often seen as
  tonality at tooth mesh frequencies, where
  penalties are given to turbines if tonal noises
  occur.
• Future state of the art will probably be MBS
  modelling.

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Questions?