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EWEA 2011 Brussels, Belgium: Europe’s Premier Wind Energy Event

EWEA 2011 Brussels, Belgium: Europe’s Premier Wind Energy Event. Structural reliability analysis of rotor blades in ultimate loading. K. C. Bacharoudis 1 , D. J. Lekou 2 , T. P. Philippidis 1 University of Patras , Dept. of Mechanical Engng & Aeronautics, Greece

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EWEA 2011 Brussels, Belgium: Europe’s Premier Wind Energy Event

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  1. EWEA 2011 Brussels, Belgium: Europe’s Premier Wind Energy Event Structural reliability analysis of rotor blades in ultimate loading K. C. Bacharoudis1, D. J. Lekou2, T. P. Philippidis1 University of Patras, Dept. of Mechanical Engng& Aeronautics, Greece Centre for Renewable Energy Sources, Wind Energy Division, Greece Brussels, 14-17 March 2011

  2. Probabilistic Strength Analysis • The objectives are: • Reliability assessment of a given design (safety factors, Target reliability) • New probabilistic design, sensitivity studies (Improve/optimize blade structural design) Brussels, 14-17 March 2011

  3. Probabilistic Strength Analysis • Sectional analysis based on thin wall multi cellular theory was performed by a numerical tool (THIN) • Monte Carlo, Edgeworth expansion method and Response Surface method/Monte Carlo were used • Stress resultants, engineering elastic constants (E1, E2 , v12 , G12) and failure stresses (XT, XC, YT, YC, S) in the principal coordinate system of the UD ply were considered random variables (RV) Brussels, 14-17 March 2011

  4. Probabilistic Strength Analysis • The effort consists of three major tasks: • Stochastic representation of material properties • Stochastic modeling of the stress resultants acting on the blade section • Implementation of fast and accurate reliability methods Brussels, 14-17 March 2011

  5. Rotor Blade Model Sec 9.2m Blade model Blade section Thin model Brussels, 14-17 March 2011

  6. Stochastic Material Properties Sec 9.2m Material properties at the ply level Laminate Blade section THIN model Material properties were considered normally distributed Brussels, 14-17 March 2011

  7. Nz z Mz Nx Ny My Mx x y • Extreme Load Analysis (IEC-61400 ed.3) Directions of the stress resultants of the blade under extreme loading Brussels, 14-17 March 2011

  8. Nz z Mz Nx Ny My Mx x y Time series from aero elastic codes • Extreme Load Analysis (IEC-61400 ed.3) Brussels, 14-17 March 2011

  9. Nz z Mz Nx Ny My Mx x y Pick local maxima according IEC 61400-1 Ed.3 Thrs.=mv+1.4*sd Extreme Load Analysis (IEC-61400 ed.3) Brussels, 14-17 March 2011

  10. Nz z Mz Nx Ny My Mx x y Find best-fit probability distributions for every mean wind speed bin • Extreme Load Analysis (IEC-61400 ed.3) Brussels, 14-17 March 2011

  11. Nz z Mz Nx Ny My Mx x y • Extreme Load Analysis (IEC-61400 ed.3) Brussels, 14-17 March 2011

  12. Nz z Mz Nx Ny My Mx x y • Extreme Load Analysis (IEC-61400 ed.3) Brussels, 14-17 March 2011

  13. Nz z Mz Nx Ny My Mx x y • Extreme Load Analysis (IEC-61400 ed.3) • Stress resultants are modeled as Gumbel distribution Brussels, 14-17 March 2011

  14. Nz z Mz Nx Ny My Mx x y Extreme Load Analysis (IEC-61400 ed.3) Correlation matrix of stress resultants for section 9.2m from root Brussels, 14-17 March 2011

  15. Nz z Mz Nx Ny My Mx x y Element failure probability i j i j Laminate • Assuming : • Laminate is a series system of layers • Each ply has one failure mode described by the specified failure criterion • Positive correlated failure modes among the layers Brussels, 14-17 March 2011

  16. Nz z Mz Nx Ny My Mx x y Element failure probability i j i j Laminate Brussels, 14-17 March 2011

  17. Nz z Mz Nx Ny My Mx x y Failure criterion i j i j Laminate Limit state function for every ply formulated by Tsai-Hahn failure criterion Brussels, 14-17 March 2011

  18. Reliability methods: Monte Carlo THIN analysis Output Variable (RV) Basic Variables (RVs) E1, E2, v12, G12 XT, XC, YT, YC, S Nx, Ny, Nz, Mx, My, Mz, Limit state function εx, εy, εs • Random number generation for the basic variables • THIN analysis • Evaluation of limit state function • Layer failure probability • Estimation of element failure probability • 2,000,000 simulations Brussels, 14-17 March 2011

  19. Reliability methods: EDW Output Variable (RV) Basic Variables (RVs) E1, E2, v12, G12 XT, XC, YT, YC, S Nx, Ny, Nz, Mx, My, Mz, Limit state function Brussels, 14-17 March 2011

  20. Reliability methods: RSM/MC Regression models Output Variable (RV) Basic Variables (RVs) εx, εy, εs (top and bottom layers) E1, E2, v12, G12 XT, XC, YT, YC, S Nx, Ny, Nz, Mx, My, Mz, Limit state function • Random number generation for the basic variables • Stress-strain analysis through regression models • Evaluation of limit state function • Layer failure probability • Estimation of element failure probability • 2,000,000 simulations Brussels, 14-17 March 2011

  21. Reliability methods: RSM/MC Regression models Output Variable (RV) Input Variables (RVs) εx, εy, εs (top and bottom layers) Limit state function E1, E2, v12, G12 Nx, Ny, Nz, Mx, My, Mz, Building regression models Design of Experiment 10 input variables 5 levels to be tested for every input variable (circumscribed CCD) 6 output parameters (strains at the lower face of the bottom and the upper face of the top ply of the laminate). 149 THIN analyses Brussels, 14-17 March 2011

  22. Failure Probability (IFF): Section 9.2m 12 20 44 48 6 41 26 1 40 45 Element # 32 [45] [45] [45] [45] [45] [-45] [90] [45] [45] [45] [45] [45] [-45] [-45] [45] [90] [-45] [90] [90] [90] [-45] [90] [90] [90] [90] [90] [90] [90] Very good agreement between MC and RSM/MC. EDW is less accurate. (Correlation was not considered) [90] [90] [-45] Layer # [90] [90] [90] [90] [90] [90] [90] [90] [90] Brussels, 14-17 March 2011

  23. Failure Probability (IFF): Section 9.2m 12 20 44 48 6 41 26 1 40 45 Element # 32 [45] [45] [45] [45] [45] [-45] [90] [45] [45] [45] [45] [45] [-45] [-45] [45] [90] [-45] [90] [90] [90] [-45] [90] [90] [90] [90] [90] [90] [90] [90] [90] [-45] Reliability analysis 3h-MC, 30 min-RSM/MC, 10 sec-EDW Layer # [90] [90] [90] [90] [90] [90] [90] [90] [90] Brussels, 14-17 March 2011

  24. Conclusions • Assessment of the reliability level of a rotor blade already designed according to IEC ed. 3 at the ply level was performed • The stochastic modeling of sectional stress resultants of the blade under extreme loading was achieved • The probabilistic analysis was performed by using MC, RSM/MC, EDW • A numerical tool was developed that can be combined with aero elastic codes and can be used for reliability analysis and probabilistic design Brussels, 14-17 March 2011

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