Fatigue Modeling of Large Composite Wind Turbine Blades

Transcription

1 Fatigue Modeling of Large Composite Wind Turbine Blades Oscar Castro K. Branner, P. Brøndsted, N. Dimitrov, P. Haselbach 4th Durability and Fatigue Advances in Wind, Wave and Tidal Energy. Bristol, UK

2 Motivation f t FATIGUE fatigue 2

3 Outline Deterministic fatigue approaches Uniaxial Multi-axial Probabilistic fatigue approaches Uniaxial Multi-axial Conclusions and future work 3

4 Deterministic and uniaxial approach Based on IEC standard and DNV GL certification and design guidelines Design Load Cases for fatigue: 2 DLC 1.2: Power production (NTM) DLC 2.4: Power production plus occurrence of fault (NTM) 1 DLC 3.1: Start up (NWP) 6 DLC 4.1: Normal shut down (NWP) DLC 6.4: Parked (NTM) 1 (t) Design lifetime: 2 years 1 min average wind speed simulations No. seeds: 15 2 (t) 6 (t) Philippidis_Vassilopoulos_Part2_IJF_22 4

5 Current standard method Uniaxial Rainflow cycle counting Stress time series calculation σ 1 (t) Cycle counting n 1, σ m,1, σ a,1 n 3, σ m,3, σ a,3 n n, σ m,j, σ a,k Constant Life Diagrams Goodman diagrams (Linear) N Fatigue Failure Criteria Damage summation Palmgren-Miner rule (Linear) (2 years) 5

6 Implemented cross section fatigue tool BECAS Geometry and layup Stress time series calculation Material properties HAWC2 Aeroelastic loads Cycle counting Constant Life Diagrams HAWC2 (Horizontal Axis Wind turbine simulation Code 2nd generation) BECAS (BEam Cross section Analysis Software) Fatigue Failure Criteria Damage summation 6

7 Study case: NREL 5 MW RWT spar caps Span: 1.5 m DLC 1.2: Power production (NTM) Wind direction: degress No. seeds:6 Lifetime: 2 years A. Material properties of Glass (UD) were taken from OptiDAT database B. A. Suction side spar cap Glass(UD) B. Pressure side spar cap 7

8 Cumulative damage at spar caps D X1-2 2X1-2 D Rear shear web Rear shear web Front shear web Front shear web 8

9 Deterministic and multi-axial approach Multi-axial Rainflow cycle counting Stress time series calculation σ 1 (t) σ 2 (t) σ 6 (t) n 1, σ m,1, σ a,1 Cycle counting Piecewise linear n 3, σ m,3, σ a,3 n n, σ m,j, σ a,k CLD Multi-axial fatigue criterion Fatigue Failure Criteria Damage summation Palmgren-Miner rule (Linear) (2 years) 1

10 σ 6 [Pa] σ 1 [Pa] σ 2 [Pa] Stress time series 4 2 x1 7 Longitudinal 12 1 x1 5 Transverse Time step x In-plane shear Stress time series for mesh element No 455 obtained by using BECAS. 1 min of simulation for a wind speed of 13 m/s and DLC Fatigue 5 modeling 1 of large 15 composite 2 25 Time step

11 Constant life diagrams Longitudinal direction Transverse direction Experimental data from OptiDAT Database Glass(UD) In-plane shear 12

12 Fatigue failue criteria Failure Tensor Polynomial in Fatigue (FTPT) 2 σ 1amp X 2 N + σ 2 2amp Y 2 N σ 1ampσ 2amp X N Y N + σ 2 6amp S 2 N 1 = N Where X N, Y N and S N denote the corresponding S-N curves For correlated σ 1amp, σ 2amp and σ 6amp a linear relationship can be defined: σ jamp = ρ σ1 σ j σ 1amp Std σ1 Std σj σ jmean = μ σj +ρ σ1 σ j σ 1amp μ σ1 Std σ1 Std σj j = 2 or 6 According to Gardoni & Der Kiureghian ρ σ1 σ j.7 13

13 σ 1 [Pa] σ 1 [Pa] Correlation between σ 1 and σ 2 Suction side spar cap Evaluated mesh element 13 m/s 25 m/s ρ σ1 σ 2 = 1 ρ σ1 σ 2 = 1 σ 2 [Pa] σ 2 [Pa] Correlation factors ρ σ1 σ 2 from 1-min simulations for wind speed of and DLC

14 Re-estimated 2 Wind speed of 13 m/s Wind speed of 25 m/s Re-estimated by σ 2 = μ σ2 +ρ σ1 σ 2 σ 1 μ σ1 Std σ1 Std σ2 15

15 σ 1 [Pa] σ 1 [Pa] Correlation between σ 1 and σ 6 Suction side spar cap Evaluated mesh element 13 m/s 25 m/s ρ σ1 σ 9 =.9 ρ σ1 σ 9 =.6 σ 6 [Pa] σ 6 [Pa] Correlation factors ρ σ1 σ 6 from 1-min simulations for wind speed of and DLC

16 Re-estimated 6 Wind speed of 13 m/s Wind speed of 25 m/s Re-estimated by σ 6 = μ σ6 +ρ σ1 σ 6 σ 1 μ σ1 Std σ1 Std σ6 17

17 Cumulative damage at pressure side spar cap D 1 D 1 Rear shear web Front shear web A. Multi-axial approach.1 B. Uniaxial approach.1 Results follow the trends found by Philippidis_Vassilopoulos_IJF_22 Underestimation of the cumulative damage when transverse and in-plane share stresses are neglected Possible overestimation of the cumulative damage when multi-axial criterion is applied 18

18 Cumulative damage at suction side spar cap D D Rear shear web.7.7 Front shear web A. Multi-axial approach.1 B. Uniaxial approach.1 Results follow the trends found by Philippidis_Vassilopoulos_IJF_22 Underestimation of the cumulative damage when transverse and in-plane share stresses are neglected Possible overestimation of the cumulative damage when multi-axial criterion is applied 19

19 Probabilistic approaches X GEOM Geometry and layup Stress time series calculation X str Material properties X elas; X stren; X SN Cycle counting X RFC X L Aeroelastic loads CLD X CLD X FFC Fatigue Failure Criteria Limit state equation X: uncertainty variables X PMR Damage summation Probability of failure 2

20 Limit state equation g X = D failure D X g X = X PMR X L m X str m X RFC m D X Where D(X) is the cumulative damage, X L = X load X st X exp X aero X dyn X sim X geom and m = 1 Relaibility method: Monte Carlo (sample size of 1) to estimate index values and P f = Φ β Model uncertainties on aeroelastic fatigue loads and on the fatigue analysis process [Tarp-Johansen_ASME_25, Tarp- Johansen_Riso_23, Dimitrov_PhdThesis_DTU_213] Loads Fatigue analysis Name Description Distribution μ, σ X load Load carrying capacity Deterministic (1.;.) X st Limited wind data Lognormal (1.;.5) X exp Exposure Lognormal (1.;.1) X aero Airfoil coefficients Gumbel (1.;.1) X dyn Dynamics Lognormal (1.;.5) X sim Simulation Normal (1.;.5) X geom Normal Normal (1.;.3) X str Stress analysis Lognorm (1.;.5) X RFC Rainflow count Lognorm (1.;.2) X PMR Palmgren-Miner rule Lognorm (.33;.21) 21

21 Probability of failure at pressure side spar cap P f 1 P f 1 Rear shear web Front shear web A. Multi-axial approach.1 B. Uniaxial approach.1 Results consistent with deterministic ones Underestimation of probability of failure when transverse and in-plane share stresses are neglected Possible overestimation of probability of failure when multi-axial criterion is applied 22

22 Probability of failure at suction side spar cap P f P f Rear shear web Front shear web A. Multi-axial approach.1 B. Uniaxial approach.1 Results consistent with deterministic ones Underestimation of probability of failure when transverse and in-plane share stresses are neglected Possible overestimation of probability of failure when multi-axial criterion is applied 23

23 Effects of model uncertainties on estimated probability of failure P f P f Rear shear web Front shear web A. Multi-axial (Model uncertainties).1 B. Multi-axial (Not model uncertainties).1 High effects of model uncertainties on the probability of failure 24

24 Conclusions The fatigue response of the spar caps was analyzed by implementing both deterministic and probabilistic approaches. For both cases, uniaxial and multi-axial fatigue approaches were implemented. Correlation factors between axial stresses and both transverse and in-plane shear stresses of the blade were used to apply the fatigue multi-axial criterion. The cumulative damage (uniaxial case) and the probability of failure (multi-axial case) were underestimated by applying uniaxial fatigue approaches and possibly overestimated by applying multi-axial approaches. It was showed how the uncertainty variables have high effects on the probability of failure. 25

25 Current work X GEOM? Geometry and layup Stress time series calculation X str Statistical, physical and model uncertainties Material properties X elas; X stren; X SN? Cycle counting X RFC X L Aeroelastic loads CLD X CLD? X FFC? Fatigue Failure Criteria Limit state equation X: uncertainty variables X PMR Damage summation Probability of failure 26

26 Thanks! 27