The impact of geometric non-linearities on the fatigue analysis of trailing edge bond lines in wind turbine rotor blades

The accurate prediction of stress histories for the fatigue analysis is of utmost importance for the design process of wind turbine rotor blades. As detailed, transient, and geometrically non-linear three-dimensional finite element analyses are computationally weigh too expensive, it is commonly regarded sufficient to calculate the stresses with a geometrically linear analysis and superimpose different stress states in order to obtain the complete stress histories. In order to quantify the error from geometrically linear simulations for the calculation of stress histories and to verify the practical applicability of the superposition principal in fatigue analyses, this paper studies the influence of geometric non-linearity in the example of a trailing edge bond line, as this subcomponent suffers from high strains in span-wise direction. The blade under consideration is that of the IWES IWT-7.5-164 reference wind turbine. From turbine simulations the highest edgewise loading scenario from the fatigue load cases is used as the reference. A 3D finite element model of the blade is created and the bond line fatigue assessment is performed according to the GL certification guidelines in its 2010 edition, and in comparison to the latest DNV GL standard from end of 2015. The results show a significant difference between the geometrically linear and non-linear stress analyses when the bending moments are approximated via a corresponding external loading, especially in case of the 2010 GL certification guidelines. This finding emphasizes the demand to reconsider the application of the superposition principal in fatigue analyses of modern flexible rotor blades, where geometrical nonlinearities become significant. In addition, a new load application methodology is introduced that reduces the geometrically non-linear behaviour of the blade in the finite element analysis

Model updating of wind turbine blade cross sections with invertible neural networks

Fabricated wind turbine blades have unavoidable deviations from their designs due to imperfections in the manufacturing processes. Model updating is a common approach to enhance model predictions and therefore improve the numerical blade design accuracy compared to the built blade. An updated model can provide a basis for a digital twin of the rotor blade including the manufacturing deviations. Classical optimization algorithms, most often combined with reduced order or surrogate models, represent the state of the art in structural model updating. However, these deterministic methods suffer from high computational costs and a missing probabilistic evaluation. This feasibility study approaches the model updating task by inverting the model through the application of invertible neural networks, which allow for inferring a posterior distribution of the input parameters from given output parameters, without costly optimization or sampling algorithms. In our use case, rotor blade cross sections are updated to match given cross-sectional parameters. To this end, a sensitivity analysis of the input (material properties or layup locations) and output parameters (such as stiffness and mass matrix entries) first selects relevant features in advance to then set up and train the invertible neural network. The trained network predicts with outstanding accuracy most of the selected cross-sectional input parameters for different radial positions; that is, the posterior distribution of these parameters shows a narrow width. At the same time, it identifies some parameters that are hard to recover accurately or contain intrinsic ambiguities. Hence, we demonstrate that invertible neural networks are highly capable for structural model updating

Model updating of a wind turbine blade finite element Timoshenko beam model with invertible neural networks

Digitalization, especially in the form of a digital twin, is fast becoming a key instrument for the monitoring of a product's life cycle from manufacturing to operation and maintenance and has recently been applied to wind turbine blades. Here, model updating plays an important role for digital twins, in the form of adjusting the model to best replicate the corresponding real-world counterpart. However, classical updating methods are generally limited to a reduced parameter space due to low computational efficiency. Moreover, these approaches most likely lack a probabilistic evaluation of the result. The purpose of this paper is to extend a previous feasibility study to a finite element Timoshenko beam model of a full blade for which the model updating process is conducted through the novel approach with invertible neural networks (INNs). This type of artificial neural network is trained to represent an inversion of the physical model, which in general is complex and non-linear. During the updating process, the inverse model is evaluated based on the target model's modal responses. It then returns the posterior prediction for the input parameters. In advance, a global sensitivity study will reduce the parameter space to a significant subset on which the updating process will focus. The finally trained INN excellently predicts the input parameters' posterior distributions of the proposed generic updating problem. Moreover, intrinsic model ambiguities, such as material densities of two closely located laminates, are correctly captured. A robustness analysis with noisy response reveals a few sensitive parameters, though most can still be recovered with equal accuracy. And, finally, after the resimulation analysis with the updated model, the modal response perfectly matches the target values. Thus, we successfully confirmed that INNs offer an extraordinary capability for structural model updating of even more complex and larger models of wind turbine blades

Validation of a modeling methodology for wind turbine rotor blades based on a full-scale blade test

Detailed 3D finite-element simulations are state of the art for structural analyses of wind turbine rotor blades. It is of utmost importance to validate the underlying modeling methodology in order to obtain reliable results. Validation of the global response can ideally be done by comparing simulations with full-scale blade tests. However, there is a lack of test results for which also the finite-element model with blade geometry and layup as well as the test documentation and results are completely available. The aim of this paper is to validate the presented fully parameterized blade modeling methodology that is implemented in an in-house model generator and to provide respective test results for validation purpose to the public. This methodology includes parameter definition based on splines for all design and material parameters, which enables fast and easy parameter analysis. A hybrid 3D shell/solid element model is created including the respective boundary conditions. The problem is solved via a commercially available finite-element code. A static full-scale blade test is performed, which is used as the validation reference. All information, e.g., on sensor location, displacement, and strains, is available to reproduce the tests. The tests comprise classical bending tests in flapwise and lead–lag directions according to IEC 61400-23 as well as torsion tests. For the validation of the modeling methodology, global blade characteristics from measurements and simulation are compared. These include the overall mass and center of gravity location, as well as their distributions along the blade, bending deflections, strain levels, and natural frequencies and modes. Overall, the global results meet the defined validation thresholds during bending, though some improvements are required for very local analysis and especially the response in torsion. As a conclusion, the modeling strategy can be rated as validated, though necessary improvements are highlighted for future works

Fatigue properties of a structural rotor blade adhesive under axial and torsional loading

Axial and torsional fatigue tests at different stress ratios were performed on a structural adhesive designed for wind turbine rotor blades. By employing previously optimized specimens, fatigue properties were recorded without influences of manufacturing-induced defects such as pores. The Stüssi S–N model was an excellent fit to the data and was combined with a Haibach extension line to account for uncertainties in the gigacycle fatigue regime. A comparison of the results with hand-mixed specimens revealed significant and load level-dependent differences, indicating that manufacturing safety factors should be applied to the slope of the S–N curve. The experiments were accompanied by stiffness degradation measurements, which enabled an analysis of Young's and shear modulus degradation interactions. The degradation was modeled using power law fits, which incorporated load level-dependent fitting parameters to allow for a full description of the stiffness reduction and a prediction of the residual fatigue life of run-out specimens

Design and manufacturing optimization of epoxy-based adhesive specimens for multiaxial tests

Specimen design and manufacturing quality are decisive factors in the experimental determination of material properties, because they can only be reliably determined if all undesired influences have been minimized or are precisely known. The manufacture of specimens from highly viscous, two-component and fiber-reinforced structural adhesives presents a challenge from this point of view. Therefore, a design and manufacturing optimization procedure for fiber-reinforced structural adhesives and multiaxial testing was developed. It incorporated a finite element parametric study to minimize stress concentrations in the specimen geometry. Vacuum speed mixing was combined with 3D printed mold inserts to enable the manufacture of homogeneous specimens with negligible porosity. The method was demonstrated by means of a structural adhesive used to manufacture wind turbine rotor blades, while the manufacturing quality was verified with high-resolution X-ray microscopy (μCT scanning), enabling detailed detection of pores and geometrical imperfections. The results of uniaxial and biaxial static tests show maximized strength and stiffness properties, while the scatter was minimized in comparison to that stated in international literature. A comparison of the mechanical properties and associated manufacturing techniques is given. The comparison includes a porosity analysis of a specimen from an industrial dosing machine used for rotor blade manufacture. © 2021 The Author(s

On the impact of multi-axial stress states on trailing edge bondlines in wind turbine rotor blades

For a reliable design of wind turbine systems all of their components have to be designed to withstand the loads appearing in the turbine's lifetime. When performed in an integral manner this is called systems engineering, and is exceptionally important for components that have an impact on the entire wind turbine system, such as the rotor blade. Bondlines are crucial subcomponents of rotor blades, but they are not much recognized in the wind energy research community. However, a bondline failure can lead to the loss of a rotor blade, and potentially of the entire turbine, and is extraordinarily relevant to be treated with strong emphasis when designing a wind turbine. Modern wind turbine rotor blades with lengths of 80 m and more offer a degree of flexibility that has never been seen in wind energy technology before. Large deflections result in high strains in the adhesive connections, especially at the trailing edge. The latest edition of the DNV GL guideline from end of 2015 demands a three-dimensional stress analysis of bondlines, whereas before an isolated shear stress proof was sufficient. In order to quantify the lack of safety from older certification guidelines this paper studies the influence of multi-axial stress states on the ultimate and fatigue load resistance of trailing edge adhesive bonds. For this purpose, detailed finite element simulations of the IWES IWT-7.5-164 reference wind turbine blades are performed. Different yield criteria are evaluated for the prediction of failure and lifetime. The results show that the multi-axial stress state is governed by span-wise normal stresses. Those are evidently not captured in isolated shear stress proofs, yielding non-conservative estimates of lifetime and ultimate load resistance. This finding highlights the importance to include a three-dimensional stress state in the failure analysis of adhesive bonds in modern wind turbine rotor blades, and the necessity to perform a three-dimensional characterization of adhesive materials

Technical note: Estimation of real rabbit meat consumption in Italy

[EN] As in other livestock species, the annual per capita consumption of rabbit meat is currently estimated as the ratio of the total weight of carcasses available for consumption to the number of inhabitants of a certain region. The aim of this work was to establish conversion coefficients from carcass to dible lean meat and estimate real rabbit meat consumption in Italy. Accordingly, a total of 24 rabbits were slaughtered at 2 different ages to obtain carcasses representative of the main market categories in Northern Italy: medium-size (carcass weight of about 1.4 kg) and heavy-size (carcass weight of about 1.8 kg). Chilled carcasses were used to determine offal, dissectible fat, bone and meat weights and yields. Experimentally obtained conversion factors from carcass to edible lean meat and estimated meat waste percentage at retail and consumption levels were subsequently used to estimate the real per capita amount of rabbit meat consumed in Italy. The finding of this study revealed that, if compared to the medium-size group, heavy-size carcasses had higher lean meat yield for both intermediate (92.9 vs. 92.4%; P<0.05) and hind parts (84.3 vs. 79.1%; P<0.001). On the contrary, the meat yield of fore part was higher in the medium-size group (66.2 vs. 65.5%; P<0.001) compared to heavy-size carcasses. Eventually, overall meat yield was higher in heavy-size carcasses compared to medium-size ones (64.4 vs. 63.2%; P<0.001). By using these conversion factors and estimated overall losses at retailing and home-consumption (15%), we estimated that real per capita annual rabbit meat consumption is 0.50 kg in Italy, which is only 54% compared to the estimated apparent consumption (0.90 kg).Petracci, M.; Soglia, F.; Baldi, G.; Balzani, L.; Mudalal, S.; Cavani, C. (2018). Technical note: Estimation of real rabbit meat consumption in Italy. World Rabbit Science. 26(1):91-96. doi:10.4995/wrs.2018.7802SWORD919626

An open-source framework for the uncertainty quantification of aeroelastic wind turbine simulation tools

The uncertainty quantification of aeroelastic wind turbine simulations is an active research topic. This paper presents a dedicated, open-source framework for this purpose. The framework is built around the uncertainpy package, likewise available as open source. Uncertainty quantification is done with a non-intrusive, global and variance-based surrogate model, using PCE (i.e., polynomial chaos expansion). Two methods to handle the uncertain parameter distribution along the blades are presented. The framework is demonstrated on the basis of an aeroelastic stability analysis. A sensitivity analysis is performed on the influence of the flapwise, edgewise and torsional stiffness of the blades on the damping of the most critical mode for both a Bladed linearization and a Bladed time domain simulation. The sensitivities of both models are in excellent agreement and the PCE surrogate models are shown to be accurate approximations of the true models