Question

Consider the blade of the wind turbine (Fig. 2, next page), having the following properties:

Blade radius, R=19.0 m Rotor angular speed,

Ω=5.0 rad/s Blade total mass, Mb=900 kg Offset, eR (additional information below)

Hinge spring stiffness, 7*10⁶ (N-m/rad)

See Fig. 2 on the next page

Consider the blade of the wind turbine (Fig. 2, next page), having the following properties: Blade radius, R-19.0 m Rotor angular speed, Ω 5.0 rad/s Blade total mass, M, 900 kg Offset, eR (additional information below) Hinge spring stiffness, Kg7 x 10° (N-m/rad) See Fig. 2 on the next page a) Write te flapping motion equation of the blade with e 0 subjected to te centrifugal force (gravitational force is neglected). Find the non-rotating and rotating natural frequencies of the blade b) Write the flapping motion equation of the blade with e-0.15, subjected to the centrifugal force (gravitational force is neglected). Find the solution of the flapping motion of the blade with initial conditions: β(0)-0.03rad, β(0)-0.1 rads. Find the flapping angle at r-ss. Could you also find the maximum tip flapping displacement under these conditions c) Write the flapping motion equation of the blade with e=0.15, subjected to both centrifugal and gravitational forces. Find the rotating natural frequency of the blade when the azimuthal angle is equal to -30 deg, i.e. assuming that the blade is "quasi-statically" or slowly rotating in the vertical plane compared to the out-of plane flapping oscillatio d) Write the same flapping motion equation as in item (c) but with the azimuthal angle V depending on time , as follows: Ψ(1)-ΩΉΌ (Ψα initial angle). Please briefly discuss the possibility of solving this equation with variable V(t) (What is strange about this equation? How would you examine this equation? Can you determine the flapping frequency?) Azimuthal angle K, M, eR (1-e)R Fig. 2. Hinge-spring blade model

Answer 1

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