Wind_Energy_Essentials_Lecture 6b

# Wind_Energy_Essentials_Lecture 6b - Structural Analysis of...

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11/9/2010 1 Structural Analysis of Wind Turbines Loads gravity Wind pressure

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11/9/2010 2 Special Considerations Concerning Loads •Storm winds •Sudden gusts •Turbulence •Earthquake loads •Waves (offshore turbines) •TIME DEPENDENCE(dynamics) •Control forces Effects of Loads (Deformation and Stresses) l l σ lt σ t σ lt σ lt σ lt σ t σ l σ
11/9/2010 3 Failure Mechanisms square4 Rapture square4 Buckling square4 Fatigue strength effective σ σ = critical material geometry f σ σ = ) , , ( const cycles of glyph817 design g = ) , , ( σ Rapture l l σ lt σ t σ lt σ lt σ lt σ t σ l σ . , , . . max etc g e Mises effective effective strength effective σ σ σ σ σ σ = = = Rapture line

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11/9/2010 4 Buckling l l σ lt σ t σ lt σ lt σ lt σ t σ l σ critical t L E E f σ ν σ = ,...) , , , , , ( 2 1 Fatigue Its effects are similar to rapture but occur for strength effective σ σ This is particularly important for wind turbines where the loads are always oscilatory
11/9/2010 5 Basic Elements of Stress Analysis (Single Degree of Freedom) Second Newton’s Law M k F (t) u (t) M S (t)=k u (t) F (t) M u •• =F (t)-k u (t) (“stress” in the spring) W R Free body diagram No friction Basic Elements of Stress Analysis (Free Vibration ) M u •• =F (t)-k u (t) F (t)=0 M u •• +k u (t)=0 u (t)= U sin(ωt) (-ω 2 M +k) U sin(ωt)=0 ω=(k/M) 1/2 ω-”circular” frequency of vibrations No forcing term

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11/9/2010 6 Basic Elements of Stress Analysis (Flow Induced Motion) M k F u (t) v a F (v F ,u,ρ F ) M u •• =F (v a ,u,ρ a ))-k u (t) and Wind Equations(v a ,u,ρ a )=0 F results from wind-structure interaction Stress Analysis of Turbine (Multibody Dynamics) DEFORMABLE BLADES DEFORMABLE TOWER RIGID GEAR BOX v a DEFORMABLE TRANSMISSION SHAFT (inside the box)
11/9/2010 7 Stress Analysis of Turbine (The Main Difficulty) 1. Design of the turbine (blades) depends on the load and the load depends on the design 2. Precise description leads to huge system of equationas (for combined air and structure system) Iterative and approximate approach is needed DEGREE OF APPROXIMATION DEPENDS ON THE PURPOSE OF ANALYSIS Stress Analysis of Turbine (Basic Form of Equations, Approximations Used) TURBINE MODEL Mu •• =F(u,v a, ρ a )-Ku mass matrix Flow induced forcing vector Stiffness matrix vector of kinematic degrees of freedom (displacements) Approximations: the blade, tower and the shaft are often modeled using only few modal parameters (4 for each blade, 2 for tower and 1 for shaft). Characterization

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