Keywords

33.1 Introduction

In the past decades rotor blade designs of wind turbines have been thoroughly investigated by structural testing. International standards describe the validation process of the design assumptions through full-scale blade testing [11]. Therefore, blades are tested under static and fatigue loads. The static loads represent the design envelope of extreme load cases, while the cyclic loads correspond to damage equivalent fatigue loads of at least 20 years of operation. A cyclic full-scale blade test in resonance excitation, however, is reaching its limits when it is used to investigate the structural response under combined flap- and lead-lag loading scenarios subjected to specific stress ratios [17].

As a supplement to the full-scale blade experiment, testing of representative blade elements and sub-components is presented as a design validation method for rotor blades in widely accepted guidelines [9]. Generic elements and structures have been developed for this purpose, e. g. [1, 13, 19]. In the present research, however, a sub-component is considered as a structural part cut directly out of a wind turbine rotor blade [12]; it therefore corresponds to the blade full-scale.

Berring et al. [2] worked on the determination of the bend-twist effect and tested an outboard blade segment. Finite element (FE) simulations of the test were conducted using shell and volume elements to obtain a reasonable representation of the torsional behavior of the specimen [7]. Furthermore, Ridzewski [15] proposed a setup for testing the leading edge of a wind turbine blade. Lahuerta et al. [14] presented experimental results of a wind turbine blade segment test with clamped edges focusing on the structural performance of the trailing edge. With this configuration it is possible to introduce the applied bending moment of a cross-section as in a full-scale test. Moreover, Branner et al. [8] presented a similar test concept, but cutting the blade along the spar cap. In that context a segment/sub-component test configuration with flexible edges was introduced by Rosemeier et al. [18]. The aim was to impose a strain distribution along and across the sub-structure similar to the corresponding full-scale blade test.

Analytical and numerical results of this sub-component test concept are presented in this work and further compared to deformation measurements recorded with electrical strain gauges and a digital image correlation system.

33.2 Methodology

33.2.1 Testing Concept

The proposed test concept is designed with a single actuator (Fig. 33.1) allowing the flexible adjustment of combined static and fatigue loading scenarios for blade sub-components, which are either cut out of a full-scale blade or manufactured separately.

Fig. 33.1
figure 1

Side view of the setup (a): a segment cut cross-section (black) of a full cross-section (grey) is cut out and clamped between ball joint R and T. Ball joint T is connected to a strong wall. Ball joint R is connected to vertical beam, which is mounted to a strong floor at hinge B. An adjustable actuator connects the beam at joint D with another stiff wall at joint C. The front view into plane A-A is shown in (b) [18]

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The specimen is glued into load frames at its span-wise edges, which are mounted to ball joints R and T. Joint T is mounted to a stiff wall and joint R is mounted to a vertical beam that is hinged on a strong floor at joint B. The actuator is mounted between another stiff wall (joint C) and the vertical beam (joint D) allowing for a flexible positioning along the height, which makes it possible to operate the actuator in its most efficient position w. r. t. force and displacement. The concept allows the adjustment of the following parameters: (a) the distance between the axis through ball joints R and T (RT-axis), and the line of centroids \(z_{\text{c}}^{\prime }\) defines the bending moment distribution M along the specimen due to an eccentrically introduced force F, and (b) the superposition of the resulting normal force distribution N and M defines the target strain distribution across the cross-section. This concept is described in detail by Rosemeier et al. [16, 18]. The shape of the bending moment distribution depends on the shape of the line of centroids \(z_{\text{c}}^{\prime }\), which can be influenced by the shape of the specimens cut along the span or by addition of material or springs connected in parallel to the specimen.

33.2.2 Models

The structural response of the ball-joint sub-component test concept is analyzed using the example of a 34 m blade design. The trailing edge sub-component of approximately 3 m length was virtually cut out, such that the target cross-sections in the middle of the specimen is at 71 % blade length. The segment was further cut in span-wise direction such that only the area of interest remains, i.e. the trailing edge cell including one main shear web. An analytical beam model (AM) on the basis of Euler-Bernoulli beam theory [10] was assembled with cross-section properties determined by the Beam Cross Section Analysis Software BECAS [3,4,5,6]. Additionally, finite element shell models (FEM) of the full-scale blade test and the sub-component test setup were implemented in ANSYS APDL [20]. The blade parameterization and input generation for the models was conducted using workflows of the FUSED-Wind framework [22].

The positions of the load introduction points at the specimen edges (Fig. 33.2d) were determined using the analytical model of the full and the cut cross-section. The structural response of the static full-scale leading-to-trailing edge (LTT) load case was chosen as reference.

Fig. 33.2
figure 2

Finite element model showing extruded SHELL281 elements of the tested 3 m section (a), a zoom into the trailing edge bond-line modelled with SOLID186 elements (b), the load frame representation by CERIG elements and the load introduction via a master node (c) and its structural strain response (d). The color scale shows the longitudinal strain ε z along the specimen at 20 % load level of the final test load of the leading-to-trailing edge (LTT) load case

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33.2.3 Experimental

33.2.3.1 Setup

The test concept described in Sec. 33.2.1 was set up on a strong floor with two adjustable strong walls (Fig. 33.3). The hydraulic actuator was used in displacement control and had a nominal load of 210 kN with a maximum stroke displacement range of 600 mm. A benefit of this setup is that relatively small variations in specimen length can be compensated by the stroke displacement. The ball joints used were designed for a nominal load of 400 kN. The gravity load constrains the 3 m long specimen’s rotational degree of freedom about its length axis. While mounting the specimen, it finds its stable position depending on the position of both joints R and T within the cross-section.

Fig. 33.3
figure 3

Test rig overview (a) and specimen view (b). The hydraulic actuator is shown on the left introducing the loading into a hinged vertical beam. The specimen is mounted via ball joints between the vertical beam and a strong wall on the right. In the front two of the four DIC cameras are seen facing the suction side of the specimen

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33.2.3.2 Specimen Preparation

The specimen was cut along the spar cap and ground at the load introduction zones (Fig. 33.4a) both to improve the adhesion with the load frames and enhance visual inspections during testing (Fig. 33.4b). Wooden frames were milled according to the outer and inner surface of the specimen. In a casting process (Fig. 33.4c) the frames were glued to the specimen with an epoxy system. The curing of the epoxy resin was performed approximately for 12 h at 65 ∘C.

Fig. 33.4
figure 4

Ground of the paint at the load introduction zones (a) as well as on the trailing edge bond line (b). Root and tip ends of the specimen were glued into wooden load frame using a casting process

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33.2.3.3 Measurement Equipment

33.2.3.3.1 Strain Gauges

Strain gauges (SG) were applied according to the coordinate system as shown in Fig. 33.5, where the relative arc-length coordinate s starts at the trailing edge of the pressure side surface going towards the leading edge and ending at the trailing edge of the suction side surface. The s-coordinate is parallel to the load frames and the z-coordinate is perpendicular to the load frames pointing from the root towards the tip end. The load frames were mounted such that they were positioned parallel to the virtual root coordinate system of the full-scale blade.

Fig. 33.5
figure 5

Specimen coordinate system in suction side view. Root end is on the left and tip and on the right hand side

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33.2.3.3.2 Digital Image Correlation

In addition to strain gauge measurements, a stereo digital image correlation (DIC) system measured the specimen movement [23], providing out-of-plane displacement and full-field strain of the entire specimen surface. A black and white stochastic speckle pattern was painted on both specimen surfaces (Fig. 33.6a). Flags were placed on the wood frame visible by all cameras, such that the cameras were coupled into a single, global coordinate system during post-processing.

Fig. 33.6
figure 6

Speckle pattern for the digital image correlation (DIC) system shown on the suction side surface (a) and virtual strain gauge positions (b). Three reference markers are positioned at the trailing edge and spar cap edge of the specimen to define the common coordinate system for suction and pressure side. Post-processing lines are defined along the target cross-section (TCS-line) and along the middle of the trailing edge cell (TEC-line). Additionally, the trailing edge electrical strain gauge line (TE-line) is highlighted. The color scale in (b) shows the longitudinal strains ε z

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Two pairs of 2.8 megapixel cameras were installed to record the movement of each panel separately - two cameras on the SS and two on the PS. The use of two stereo DIC setups and a global coordinate system provided the ability to measure out-of-plane displacements of both panels relative to the other.

Virtual strain gauges placed next to the electrical strain gauges compared the TCS-line (Fig. 33.6b).

33.3 Experimental Results and Model Validation

33.3.1 Geometry Comparison

The comparison of the finite element model (FEM) with the measured geometry of the specimen shows that the FEM is thicker compared to the actual geometry (Fig. 33.7).

Fig. 33.7
figure 7

Geometry comparison of the finite element model and actual blade geometry at the tip end of the sub-component specimen

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33.3.2 Strain Response Along the Trailing Edge

The trailing edge specimen was loaded in a configuration aiming to reach the 100 % strain level of the leading-towards-trailing edge (LTT) full-scale blade test load case [21]. The trend of the longitudinal strains measured with strain gauges (SG) at the trailing edge pressure (PS) and suction side (SS) (TE-line at s ≈50 mm, see Fig. 33.6a) are in a good agreement with the measured values of the LTT full-scale test (Fig. 33.8a). The slope of the strain distribution along the trailing edge was successfully replicated. The discrepancy close to the load frames is caused from the stiffening of the support wooden blocks. Moreover, the back to back values at both sides of the TE compare very well to each other. At the target cross-section of the specimen they move apart indicating a bending deformation of an S-shape.

Fig. 33.8
figure 8

Validation of the finite element (FEM) and analytical (AM) model of the full-scale blade (FST) and sub-component ball joint concept (BJ-SCT). The models are benchmarked with the full-scale experiment [21] and the sub-component experiments using the full-scale leading-to-trailing edge (LTT) load case at 100 % load level. The longitudinal strain ε z is compared for both pressure and suction side along the trailing edge bond line (a) and along the target cross-section surface coordinate s (b)

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The analytical (AM) and finite element models (FEM) are validated against the experimental, longitudinal strains along the specimen length. The strain data were derived from SGs. The longitudinal strain along the trailing edge bond-line is benchmarked (Fig. 33.8a). In general, it can be seen that the experimental strain level in both full-scale test (FST) and ball-joint sub-component test concept (BJ-SCT) is lower compared to the FEM, but for both experiments the strain is at the same level. The relative strain trend between suction (SS) and pressure side (PS), the pathway of the FEM and experiment BJ-SCT is similar: Along the length the strain level on the PS is getting lower than on the SS, finding its peak value at the target cross-section at ≈24 m blade length. Strain peaks were recorded next to both load frames as also prognosed by the FE model The peaks are caused by the load frame constraints on to the local Poisson’s ratio of the structure.

33.3.3 Strain Response Across the Target Cross-section

The longitudinal strain across the cross-section coordinate s (Fig. 33.9a) is observed at the target cross-section in the middle of the specimen at about 24 m blade length. The strain level of the BJ-SCT experiment is in a good agreement with the FEM and AM results. The experimental strain level on the SS, however, is lower than the level observed in the FEM and AM. The slightly increased strain dimple at s = 0.83 correlates well to the trend of the convex strain distribution in the BJ-SCT FE model.

Fig. 33.9
figure 9

Validation of the finite element (FEM) and analytical (AM) model with sub-component ball joint concept (BJ-SCT). The models are benchmarked with the sub-component experiment using the full-scale leading-to-trailing edge (LTT) load case at 100 % load level. The longitudinal (a) and transversal (b) strain ε z is compared along the target cross-section surface coordinate s

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The longitudinal strain along the surface of the target cross-section (TCS-line) in the middle of the specimen was also monitored with SGs (Fig. 33.9a). The recordings are compared to the digital image correlation (DIC) system results at discrete points on the TCS-line. It can be seen that both measurement methods show a fair agreement regarding absolute values but they both show the same trend. The DIC strains, particularly on the PS, have a slight offset compared to the SGs, which is also the case for the mid arc-length range on the SS. The discrepancies can be explained through a spatial offset of the DIC virtual strain gauges. Moreover, the electrical strain gauges measure the local deformation and the DIC strains are a result of a smoothing algorithm over a relatively long gauge length compared to the SG length.

Furthermore, the transversal strains were extracted from SG and DIC measurements along the TCS-line (Fig. 33.9b). As in the longitudinal DIC strain results, an offset towards a lower strain level is observed on the PS compared to FEM and two SG measurement points.

33.3.4 Displacement Response

In the displacements field, u z indicates the lead-lag bending compression of the specimen (Fig. 33.10a). The compression is slightly larger on the SS compared to the PS indicating a flap-wise bending.

Fig. 33.10
figure 10

In-plane displacement u z with rigid body motion removed (a) and out-of-plane displacements u y (b) of the suction side and pressure side surface. The displacement field was extracted at 100 % test load level of the LTT load case

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The out-of-plane displacement u y along the TCS-line and along the TEC-line shows that the PS surface moves towards the SS surface, whereas the SS surface moves towards the PS surface. The whole displacement field is shown in Fig. 33.10b.

33.4 Conclusions

The structural strain response is compared to the sub-component test configuration to assess the applicability of the proposed test setup. The validation of analytical and finite element models (FEM) shows good agreement with trends seen in experimental full-scale and sub-component test results.

An advanced four camera digital image correlation (DIC) system was measuring the global deformations of the specimen. The derived DIC strain results were correlating within acceptable deviations from the electrical strain gauge recordings.

The actual blade is more flexible than the FEM since the strains along the trailing edge in the full-scale and the sub-component test are lower. This fact is supported by the geometry comparison indicating that the FEM is thicker than the actual specimen. Assuming the same structural layup and material properties, the second moment of area of the cross-section leads to a larger stiffness in the FEM. A feedback of the actual geometry into the FEM is required for a model improvement.