Wind_Energy_Essentials_Lecture 6b

Wind_Energy_Essentials_Lecture 6b - Structural Analysis of...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
11/9/2010 1 Structural Analysis of Wind Turbines Loads gravity Wind pressure
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 2
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
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 4
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
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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)
Image of page 6
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
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern