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Strain response analysis of adhesively bonded extended composite wind turbine blade suffering unsteady aerodynamic loads
Engineering Failure Analysis 85 (2018) 36–49
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Strain response analysis of adhesively bonded extended composite wind turbine blade suffering unsteady aerodynamic loads
T
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Guangxing Wua,b,c, , Zhiwen Qina,b,c, Lei Zhanga,b,c, Ke Yanga,b,c a b c
Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China Key Laboratory of Wind Energy Utilization, Chinese Academy of Sciences, Beijing 100190, China National Research and Development Center of Wind Turbine Blade, Beijing 100190, China
AR TI CLE I NF O
AB S T R A CT
Keywords: Adhesively bonding technology Extended wind turbine blade Strain response Fatigue damage Unsteady aerodynamic loads
Extending blades of wind turbine in service is the most effective method for increasing energy production. Adhesively bonding technology increases less mass and has simpler operation process, which is more suitable for extending blades in service. But unsteady aerodynamic loads on the blades due to stochastic turbulent inflow may lead to fatigue damage and even failure. This paper presented a study on strain response and fatigue life of adhesively bonded extended composite wind turbine blade suffering unsteady aerodynamic loads. Firstly, a loading method that applies periodic distributed aerodynamic loads on the blade was proposed to accurately simulate the unsteady distributed loads on the real extended blades in service. Secondly, strain response behaviors to unsteady aerodynamic loads and strain distribution behaviors in the adhesively bonded area were revealed. Finally, fatigue damage was predicted with unsteady aerodynamic load spectrums, rainflow cycle-counting algorithm, Goodman diagram and Miner's linear superposition principle. Based on the findings obtained from this study, the feasibility of adhesively bonding technology for extending blade was affirmed and a few potential future directions of study were addressed to reduce the risk of adhesively bonded structures.
1. Introduction Increasing the energy production or reducing the maintenance costs is the main way to improve the economy of wind turbines in service. In the wind turbine system, the blades are one of the most critical components to capture the power from wind. It has been well known that [1] the power output is proportional to swept area and wind speed cubed. Therefore, extending blades is one of the most effective method to harvest more wind energy in low wind speed region. Generally, there are two method to extend the wind turbine blades in service, metal bolt connection [2–4] and adhesively bonded connection [5–7]. Compared with metal bolt connection, adhesively bonded connection method has better fatigue behaviors and simpler operation process, and increases less mass, which is more suitable for the connection of composite shell structures and is discussed in this paper. Wind turbine rotors usually run in the nature atmospheric boundary layer. The stochastic turbulent inflow would induce unsteady aerodynamic loads [8,9], which are the primary source of fatigue loads in flapwise direction. How to make sure that the adhesively bonded extended composite wind turbine blade can endure the long-term unsteady aerodynamic loads? Usually, fatigue testing is conducted to verify a blade's ability to withstand its operating load spectrum over a design life of
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Corresponding author at: Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China. E-mail address: [email protected] (G. Wu).
https://doi.org/10.1016/j.engfailanal.2017.12.009 Received 16 May 2017; Accepted 6 December 2017 Available online 07 December 2017 1350-6307/ © 2017 Elsevier Ltd. All rights reserved.
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20 years [10]. The real operating load spectrum consists of more than 109 stochastic load cycles due to irregular turbulent inflow [11]. So the load spectrum is compressed into an equivalent fatigue load history of 106–107 cycles that can be applied in no more than a few months using linear damage principles [12–14]. The equivalent fatigue loads can be applied with hydraulic actuators or resonant eccentric mass [11] installed at one or several locations along the blade. However, Svensson [15] found that the fatigue load variation is an important source of scatter among material variability and other uncertainties. Lange [16] also found that fatigue reliability to be significantly affected by the type of model chosen for the loads data. The hydraulic actuators or resonant eccentric mass methods can only apply concentrated loads, which are clearly different from the distributed loads induced by flow over blades. The purpose of this work is to understand the structural response and predict fatigue damage of adhesively bonded area for extended blades suffering unsteady aerodynamic loads. An experimental method that the distributed aerodynamic loads are applied with a rotating apparatus to the extended blades was proposed and validated by computational fluid dynamics (CFD) method firstly. Secondly, strain response to pitching angle and rotating speed was analyzed, and then the distribution behaviors in the adhesively bonded area were studied. Finally, fatigue damage of adhesively bonded area for extended blades was predicted with unsteady aerodynamic load spectrums, rainflow cycle-counting algorithm [17], Goodman diagram [18] and Miner's linear superposition principle [19]. 2. Experiment setup It has been known that the turbulent inflow in the nature atmospheric boundary layer would induce unsteady aerodynamic loads. In essence, the unsteady loads are resulted from the time-variant inflow angle and speed. In this experimental investigation, a rotating apparatus was designed and ran with pitch angle and rotating speed changed in a control law to simulate the turbulent inflow conditions and generate periodic aerodynamic loads. An adhesively bonded extended blade with length of 3.5 m was designed, manufactured and tested. 2.1. Rotating experimental apparatus It is high cost to build a horizontal axis rotating apparatus for the same rotor diameter, which needs a tower and more room for the indoor test. A rotorcraft-like apparatus was designed and installed on the foundation of laboratory, as shown in Fig. 1. The weight of total apparatus without blades is about 1450 kg and the height at hub center is 1809 mm. When the 3.5 m length blades are mounted on the hub, rotor diameter will be 7674 mm. Rotating motion is driven by a 22 kW AC motor and a gearbox with ratio of 10.41. The rotating speed can be controlled by a frequency converter, and the rated output speed is 150 rpm. The rotating azimuth angle is recorded by a 12-bit encoder with resolution of 0.088°. Pitching motions of two blades are synchronously driven by a servo motor mounted on the hub with a pair of
Fig. 1. The components of rotating experimental apparatus.
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Fig. 2. Chord distributions of extended blade.
bevel gears. A thrust transducer with range of ± 1000 kg and accuracy of 0.5% F·S. was installed inside of hub and used to measure the thrust induced by rotating motion. A torque transducer with range of ± 500 Nm and accuracy of 0.5% F.S was installed between rotating motor and gearbox and used to measure the torque output of rotating motor. Most of the signals, including pitching angle, rotating azimuth angle, thrust, strains on the blades, are transmitted by a 66-channel slip ring. All the signals are sampled and processed by a Siemens S7-300 PLC module and a controlling program. 2.2. Adhesively bonded extended composite wind turbine blade 2.2.1. Geometric shape The extended blade with total length of 3.5 m comprises original blade and extended tip, as shown in Fig. 2. The original blade locates from z = 0 to 2.0 m, and extended tip locates from z = 1.6 to 3.5 m. The adhesively bonded area is from z = 1.6 to 2.0 m. The sectional shape of blade root is a rectangle with size of 160 mm by 100 mm distributed from z = 0 to 0.2 m. An airfoil, CASW1-400 shown in Fig. 3, was chosen from z = 0.52 to 3.4 m, where only the chord is different. CAS-W1-400 with thickness of 40% is one of the thick and blunt trailing-edge airfoil series designed by the Institute of Engineering Thermophysics, Chinese Academy of Sciences [20]. All of the twist angles along the extended blade are 0°. The blade coordinate is shown in Fig. 3 also. Coordinate origin locates at the intersections of rotating axis and pitching axis. The x-axis is in the rotor plane and points to trailing edge. The y-axis is perpendicular to the rotor plane and points up. The z-axis coincides with pitching axis and points from root to tip, which is not shown in Fig. 3. θ is the pitching angle between rotor plane and chord line, and is positive when the leading edge goes up as Fig. 3. 2.2.2. Structures Lay-up sequence along the blade span is shown in Fig. 4 (a). For the original blade, 4 layers of 750 tri-axial fiber and 3 layers of unidirectional fiber were stacked alternately along the total blade. And the blade root from z = 0 to 1.2 m was reinforced by 13 layers of 750 tri-axial fiber gradually. For the extended tip, only 4 layers of 750 tri-axial fiber and 3 layers of unidirectional fiber were stacked alternately along the total tip. The sectional structure except adhesively bonded area are made up of fiberglass reinforced plastic at suction side and pressure side, and adhesive at leading edge and trailing edge, as shown in Fig. 4 (b). At adhesively bonded area from z = 1.6 to 2.0 m, both pressure side and suction side of extended tip covered on the outer surface of original blade, as shown in Fig. 5. In fact, pressure side and suction side will change to each other at different pitching angle due to aerodynamic effect. However, pressure side represents the lower surface and suction side represents the upper surface at all the pitching angle in this work to avoid the confusion of names. The structural adhesive filled in the interface between original blade and extended tip. An extrusion tool was designed to make sure that the thickness of adhesive is 7 mm ± 1 mm. It is suggested from Turaga's work [21] that covering attachment would lead to about 28% improvement in initial failure strength. So the structural adhesive was 45° beveled at z = 1.6 m and a layer of 750 tri-axial fiber covered on the outer surface of adhesively bonded area. The structural adhesive is named WD3135 and purchased from Shanghai KangDa New Materials Co., Ltd. The material properties are listed in Table 1.
Fig. 3. The airfoil and coordinate used for the extended blade.
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Fig. 4. Lay-up sequence along the blade span (a), sectional structure (b).
Fig. 5. Interior structure at adhesively bonded area, spanwise section (a), chordwise section (b).
Table 1 Material properties.
Ultimate tension strength (Mpa) Ultimate compression strength (Mpa) Tensile modulus (Gpa)
UD fiber
750 Tri-axial fiber
Structural adhesive
850 500 39
320 240 17.8
52 52 4.1
2.3. Strain gauge locations set-up Strain gauges were placed at five spanwise locations of one blade, as shown in Fig. 6 (a). Section S1 locates in the original blade, and section S5 locates in the extended tip. The other three sections, S2, S3, S4, locates in the adhesively bonded area. Four strain gauges were placed in the outer surface of every sections, as shown in Fig. 6 (b). Strain gauges located at leading edge and trailing
Fig. 6. Spanwise locations (a) and chordwise locations (b) of strain gauges.
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Fig. 7. Loads applied on the blade in dynamic test case.
edge were used to monitor the change of edgewise loads, while strain gauges located at pressure side and suction side were used to monitor the change of flatwise loads. All the strain data were sampled and recorded by a strain analysis system of DH3820 with sampling frequency of 100 Hz and minimum resolution of 0.5 με. 2.4. Test cases Two test cases, quasi static case and dynamic case, were conducted in this work. In quasi static case, no pitching motion was driven and the pitching angle was kept the same when the strain values were sampled in the rotating motion. Theoretically, the aerodynamic loads are quasi steady without consider of the ground and wall effect, and the centrifugal force is constant at the same rotating speed. In this case, the mean values of strains were analyzed to investigate the effects of pitching angle and rotating speed. The flow field was validated by computational fluid dynamics (CFD) method. In dynamic case, the blade underwent rotating motion and cyclic pitching motion simultaneously. The aerodynamic loads will form unsteady flapwise moment due to cyclic change of pitching angle, as shown in Fig. 7, and the centrifugal force is almost constant at the same rotating speed. In this case, both the mean value and amplitude of strain response were investigated. The test data were used to analyze the strain distributions at the adhesively bonded area, obtain the fatigue loads, and predict the fatigue damage. 3. Aerodynamic loads analysis and validation by CFD method It has been shown from Li's data [20] that lift coefficient of CAS-W1-400 airfoil increases with the increase of angle of attack from −10° to 20°. One way to apply unsteady aerodynamic loads is to change the angle of attack periodically. Unfortunately, the real angles of attack are not known due to the induced flow by rotor motion according to wind turbine aerodynamic theory [9]. However, pitching angle is indirect related to angle of attack and can be easily controlled by pitching motor. To understand the 3D aerodynamic behaviors of the rotating blades, the CFD flow solver package ANSYS Fluent13.0 was employed to simulate the flow field and aerodynamic behaviors of rotating test. The size of computational geometric field is 10 m by 10 m by 3.65 m, which is same as the real test field. Rotating apparatus was simplified into a cylinder. The absolutely coordinate that cells of rotating apparatus and blades (pink parts) base on is fixed on the rotor, shown in Fig. 8. The interior cells and wall cells (blue parts) base on rotating coordinates and rotating speed is 150 rpm, which is same as test case. Total number of meshes is 6,617,120. The Spalart-Allmaras model was chosen as turbulent model, and the SIMPLE algorithm was chosen for coupling the momentum pressure equations. For spatial
Fig. 8. Computational geometric field and absolute coordinate. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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Fig. 9. Sectional normal force (a) and total force (b) at different pitching angle by CFD method.
discretization, a second-order upwind differencing scheme was applied. The convergence criteria for the residuals were O(10− 5) in magnitude. Sectional normal force is the integral of sectional pressure distributions by length of blade strip. The normal force direction is perpendicular to rotating plane and same as y-axis, and tangential force direction is same as x-axis in Fig. 8. Sectional normal forces increase nonlinearly from root to tip at different pitching angles as shown in Fig. 9 (a). Total forces were obtained by the integral of sectional force. It is shown from Fig. 9 (b) that normal force increases with the increase of pitching angle from −20° to 20°. No significant changes were observed about tangential force. Torque of the rotor was calculated by the measured output torque of the rotating motor and reduction ratio of the gearbox in Fig. 1. Meanwhile, rotor torque can be computed by the integral of aerodynamic force in CFD method. The comparisons of rotor torque between measurement and CFD method are shown in Fig. 10. It is indicated that the changing trends of torque along the pitching angle are almost the same. The minimum torque is observed at pitching angle of 0°. However, the measured torque is larger than numerical result at the same pitching angle. The difference may be from the mechanical losses and simplification of numerical model. Lightweight foam strips were used to visualize the flow track near ground in the rotating test and streamlines of relative velocity over the blade is extracted from the CFD results, as shown in Fig. 11. At pitching angle of − 20°, it has been observed from the foam strips that flow direction near ground points to the rotor center. The same results are revealed from streamlines by CFD method. Air from surroundings is induced to move to rotor center near ground, going up to the rooftop and flowing to the surroundings. The tip vortex flow forms with direction pointing from upper surface of blade to lower surface. It is shown from pressure contour that higher pressure distributes on the upper surface, which results in the negative normal force in Fig. 9. Correspondingly, at pitching angle of 20°, the foam strips that flow direction near ground points from the rotor center to surroundings. The tip vortex flow forms with direction pointing from lower surface of blade to upper surface. Higher pressure distributes on the lower surface, which results in the
Fig. 10. Comparisons of rotor torque between measurement and CFD.
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Fig. 11. Flow field at pitching angle of − 20° (a) and 20° (b).
positive normal force in Fig. 9. It is shown from above results that aerodynamic loads are determined by pitching angle and rotating speed. So periodic aerodynamic loads will be applied on the blades when pitching angle is changed circularly. The method is used to simulate unsteady aerodynamic load and investigate the dynamic strain response and fatigue damage of adhesively bonded extended blade. 4. Strain response 4.1. Effects of pitching angle on the mean strain in quasi static test case The strain responses to pitching angles were investigated firstly in quasi static test case. Time history of all the strains at different locations was recorded at rotating speed of 150 rpm. At every pitching angle, the mean strain value of time history was calculated and compared with each other. It is shown from Fig. 12 that with the increase of pitching angle from − 20° to 20°, the strain values at pressure side of different spanwise locations increase and the strain values at suction side decrease approximately linearly. The changes of strain values at leading edge and trailing edge are not obvious at different pitching angles. The results are consistent with the results in Fig. 9. The increase of lift will lead to the increase of flapwise moment, so strain value at pressure side will increase and strain value at suction side will decrease, as shown in Fig. 12. Besides the aerodynamic force, the blade suffers centrifugal force in the rotating motion. The aerodynamic force varies with pitching angle at the same rotating speed, while centrifugal force is almost constant. All the strain values are positive in Fig. 12, which means only the tension deflection acts on the blade. Therefore, at the pitching angle of − 20°, strain value of pressure side is positive but lower than strain value of suction side, as shown in Fig. 13. At the pitching angle of 20°, strain value of suction side is positive but lower than strain value of pressure side. 4.2. Effects of rotating speed on the mean strain values in quasi static test case It has been well known that the aerodynamic force and centrifugal force are both proportional to the square of rotor speed, as shown in the Eq. (1), where dL is the lift of blade strip; Cl is the lift coefficient; ρ is the density of air; ω is the rotor speed; dS is the area of blade strip; r is spanwise distance from rotor center; dC is the centrifugal force; dm is the mass of blade strip. 1
1
⎧ dL = Cl⋅ 2 ρv 2⋅dS = ω2⋅ 2 Cl ρr 2dS ⎨ dC = ω2r⋅dm ⎩
(1) 42
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Fig. 12. The effects of pitching angle on the mean strain values at different locations.
Fig. 13. Load analysis at different pitching angles.
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Fig. 14. The effects of rotating speed on the mean strain values and the fit curve.
So the strain value and rotor speed should present quadratic function relation. Pressure side of section S1 with maximum strain in the measured area and pressure side of section S4 with maximum strain in adhesively bonded area are focused in this section. The measured strain values at pressure side of sections S1 and S4 at pitching angle of 0° are shown by scatter in Fig. 14. The corresponding curves were fitted by quadratic polynomials. For section S1, the expression of fit curve is (2)
ε = 7.39233 + 0.77627Ω + 0.01059Ω2 with correlation coefficient of 0.99926. For section S4, the expression of fit curve is
(3)
ε = 17.49317 + 0.47674Ω + 0.00541Ω2 with correlation coefficient of 0.9997. 4.3. Time history analysis on the strain in dynamic test case
In dynamic test case, pitching angle was driven to change from − 20° to 20° with speed of 80°/s continuously, while rotating speed is 150 rpm. Time history of strain at pressure side of section S1 is shown in Fig. 15 by blue curve, and red curve represents pitching angle. The variation of strain is in tune with pitching angle, though more slight oscillations in variation of strain and phase offset show the complexity of dynamic strain response. The FFT (fast Fourier transform) algorithm is used to investigate the frequency components of strain time history in Fig. 15. It is shown in Fig. 16 (a) that strain response includes three higher-amplitude oscillations with frequency of 0.92 Hz, 2.497 Hz and 4.94 Hz. Compared with the pitching frequency of 1.1 Hz, rotating frequency 2.5 Hz, and first-order flapwise natural frequency of 5.3 Hz, the three higher-amplitude oscillations are directly related to pitching motion, rotating motion and first-order flapwise modal.
Fig. 15. Time history of strain at section S1 in cyclic pitching motion.
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Fig. 16. Frequency analysis by FFT, (a) frequency domain character, (b) bond pass filter.
There are also some high-frequency and low-amplitude oscillations. A bond pass filter from 0.5 to 5 Hz was applied to time history in Fig. 15. It is shown from Fig. 16 (b) that the strain time histories before and after the filter are almost the same, which means that the three higher-amplitude oscillations play a dominant role. 5. Strain distributions in the adhesively bonded area In dynamic test case, flapwise load varies periodically with the cyclic pitching motion. Therefore, strains at pressure side and suction side in different spanwise sections were focused to investigate the strain distributions. The average and standard deviation of strain oscillation in dynamic test case with pitching speed of 80°/s and rotating speed is 150 rpm were computed and compared. It is shown from Fig. 17 (a) that the average strain of pressure side is largest at section S1, and is smallest at section S2. The average strain increases gradually from section S2 to S5. The same variation was observed on the strains of standard deviation. At suction side, only strains at three sections from S2 to S4 were measured. The average strain increases gradually from section S2 to S4 in Fig. 17 (b), which is same as the variation of strains at pressure side. The adhesively bonded structure was considered to analyze the strain distributions in Fig. 17. It is shown in Fig. 18 that sections from S2 to S4 are in the adhesively bonded area, where the stiffness is larger than sections S1 and S5. So the strains of sections from S2 to S4 are smaller than strains of sections S1 and S5. Meanwhile, the outer surface of section S2 is close to the free end, where the local stress is minimum. Hence, the strain increases gradually from section S2 to S4 and the strain of section S2 is smallest. It is well known that the load will accumulate from blade tip to root. The load at section S5 is lower than section S1, which induces that the strain of section S5 is smaller. All the above influence factors result in the strain distributions in Fig. 17. 6. Evaluation of fatigue damage The strain at pressure side of section S4 is largest in the adhesively bonded area, and the strain at pressure side of section S1 is largest in the measuring area. In this work, the dynamic strain response at pressure side of section S4 was focused to investigate the fatigue damage of structural adhesive. The dynamic strain response at pressure side of section S1 was focused to investigate the fatigue damage of UD fiber and 750 tri-axial fiber. In the dynamic test case, the maximum rotating speed is 150 rpm, so the corresponding tip speed is 54.98 m/s. It has been summarized from Keegan's work [22] that tip speeds of wind turbine in excess of 80 m/s are now common, with many actually
Fig. 17. Strain distributions at pressure side (a) and suction side (b).
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Fig. 18. Strain distribution analysis.
exhibiting tip speeds of about 90 m/s and some select designs exceeding 100 m/s. Hence, in order to evaluate the fatigue damage of actual extended blade, the measured dynamic strain responses are needed to extrapolate from the tested tip speed to actual tip speed firstly to produce the fatigue strain spectrum. Then mean value and amplitude were counted by a cycle-counting algorithm, so-called Rainflow analysis [23]. A Goodman diagram in the guideline [10] was used to account for the effect of mean strain on the material fatigue damage and the number of tolerable load cycles was obtained by the ultimate strength. Finally, the Miner's linear superposition rule [19] was used to determine the fatigue damage. 6.1. Extrapolations of fatigue load spectrum The tested tip speed of the extended blade is 54.98 m/s, while the actual tip speed of wind turbine in rated wind speed is about 90 m/s. The measured dynamic strain response should be extrapolated from tested tip speed to actual tip speed. Firstly, rotating speed is transformed by the actual tip speed of 90 m/s with the Eq. (4), where Ω is the rotating speed, v is the tip speed, R is the distance between blade tip and rotating center.
Ω= vR
(4)
Fig. 19. Comparison of extrapolated and measured strain spectrum, (a) section S1, (b) section S4.
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Fig. 20. Rainflow cycle counting for extrapolated strain spectrum of section S1 (a) and section S4 (b).
The mean value of strain of sections S1 and S4 at the actual tip speed can be obtained by Eqs. (2) and (3), respectively. Then the multiple between the mean strain at actual tip speed and at the tested tip speed can be calculated. The multiple is 2.310 for strain of section S1, and 2.187 for strain of section S4. Finally, the extrapolated strain spectrum is the measured strain spectrum by the multiples. The comparison of extrapolated strain spectrum and measured strain spectrum is shown in Fig. 19. 6.2. Rainflow analysis The rainflow cycle counting algorithm used in this work is from a MATLAB code, which has been officially presented and described in Niesłony's work [23]. The algorithm is widely used while fatigue life assessment of structures under non-constant amplitude loading. Usually, the algorithm extract cycles from load, stress or strain history obtained from measurement or simulation. As a results of the counting several cycles and half-cycles with different amplitude and mean value are obtained. The extrapolated dynamic strain spectrums in Fig. 19 were analyzed by the rainflow cycle counting MATLAB code. The threedimensional histograms were obtained and have shown the number of cycles present in the strain spectrums of 3 min associated with a combination of the strain amplitude and the strain mean value in Fig. 20. 6.3. Fatigue damage evaluation Firstly, the stress is calculated by the Eq. (5), where σ is the stress, E is the modulus shown in Table 1, ε is the strain. (5)
σ = Eε
Then the number of tolerable load cycles at the mean value and amplitude of strain in rainflow results can be determined with the Eq. (6) in the guideline for the certification of wind turbines [10] as follows: m
Rk, t + |Rk,c| − |2⋅γMa⋅Sk, M − Rk, t + |Rk, c || ⎤ N=⎡ ⎢ ⎥ 2⋅(γMb/ C1b)⋅Sk,A ⎣ ⎦
(6)
where, Sk, M is the mean value of stress history, Sk, A is the amplitude of stress history, Rk, t is the ultimate tension strength in Table 1, Rk, c is the ultimate compression strength in Table 1, m is the slope parameter of S/N curve and is 10 for laminates with epoxy resin matrix, N is the permissible load cycle number, γMa is the partial safety factor for short-term strength of the material, γMb/C1b is the partial safety factor for fatigue strength of the material. In this work, γMa is equal to 1.35 × 1.35 × 1.1 × 1.2 × 1.1 for UD fiber and 750 tri-axial fiber and 1.35 for adhesive.γMb/C1b is equal to 1.35 × 1.1 × 1 × 1 × 1.1 for UD fiber, 1.35 × 1.1 × 1.2 × 1 × 1.1 for 750 tri-axial fiber, and 1.35 × 1 × 1.1 × 1.1 × 1.1 for adhesive. The values of γMa and γMb/C1bare determined by the description in detailed in the guideline. The number of tolerable load cycles at different amplitudes of strain oscillations are shown in Fig. 21. With the same strain amplitudes, UD fiber presents better fatigue behavior and adhesive presents worst fatigue behavior. To evaluate the fatigue damage of different materials under the unsteady aerodynamic loads, the Miner's linear superposition rule [19] was used to determine the accumulated fatigue damage in 20 years. The fatigue damage D is defined as the sum of the quotients of existing load cycle numbers ni to permissible load cycle numbers Ni, as shown in Eq. (7).
D=
n
∑ Ni i
(7)
i
It will be safe when the accumulated fatigue damage of all the materials in the extended blade is less than 1. The accumulated fatigue damages in 20 years for the three materials are shown in Table 2. All the damages are much less than 1. However, under the tested unsteady aerodynamic loads, 750 tri-axial fiber will suffer more damage and adhesive will suffer less damage, which means 47
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Fig. 21. The S/N curve results of different materials.
Table 2 Accumulated fatigue damages in 20 years.
Fatigue damage
UD fiber
750 tri-axial fiber
Structural adhesive
1.67 × 10− 5
9.21 × 10− 5
2.07 × 10− 7
that the adhesively bonded area is not the most dangerous location. It is shown that the tensile fatigue behaviors of adhesively bonded extended blade has been analyzed in this work. However, the shear strain of adhesive, which is also an important deformation type, is not measured in this test. The fatigue behavior of shear deformation in the adhesive should be investigated in the further work.
7. Conclusions An adhesively bonded extended blade was manufactured and an experimental method that the periodic aerodynamic loads are applied with a rotating and pitching apparatus was conducted to understand the structural response and predict fatigue damage of adhesively bonded extended blades. The conclusions are summarized as follows: 1) Periodic aerodynamic loads will be applied on the blades when pitching angle is changed circularly. Normal force increases with the increase of pitching angle from − 20° to 20°. No significant changes were observed about tangential force. At pitching angle of − 20°, Air from surroundings is induced to move to rotor center near ground, going up to the rooftop and flowing to the surroundings. The tip vortex flow forms with direction pointing from upper surface of blade to lower surface. The flow direction is opposite when the pitching angle is 20°. 2) With the increase of pitching angle from − 20° to 20°, the strain values at pressure side increase and the strain values at suction side decrease approximately linearly. The changes of strain values at leading edge and trailing edge are not obvious at different pitching angles. The strain value and rotating speed present quadratic function relation. The strain oscillations due to pitching motion, rotating motion and first-order flapwise modal play the dominant role in the dynamic strain response. 3) The free end, larger stiffness in adhesively bonded area and load accumulation from blade tip to root result in the strain distributions along the blade span. 4) All the materials used in the extended blade, UD fiber, 750 tri-axial fiber and structural adhesive, are safe enough in the design life of 20 years and the adhesively bonded area is not the most dangerous location. The fatigue behavior of shear deformation in the adhesive should be investigated in the further work.
Acknowledgments The project is supported by the National Natural Science Fund Youth Foundation of China (51706228), and the Research Equipment Development Project of Chinese Academy of Sciences (YZ201513).
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T. Burton, N. Jenkins, D. Sharpe, E. Bossanyi, Wind Energy Handbook, John Wiley & Sons, 2001. C.W. Kensche, Fatigue of composites for wind turbines, Int. J. Fatigue 28 (10) (2006) 1363–1374. H. Whitworth, M. Othieno, O. Barton, Failure analysis of composite pin loaded joints, Compos. Struct. 59 (2) (2003) 261–266. C. McCarthy, M. McCarthy, V. Lawlor, Progressive damage analysis of multi-bolt composite joints with variable bolt–hole clearances, Compos. Part B 36 (4) (2005) 290–305. K.S. Kim, J.S. Yoo, Y.M. Yi, C.G. Kim, Failure mode and strength of uni-directional composite single lap bonded joints with different bonding methods, Compos. Struct. 72 (4) (2006) 477–485. M.G. Song, J.H. Kweon, J.H. Choi, J.H. Byun, M.H. Song, S.J. Shin, T.J. Lee, Effect of manufacturing methods on the shear strength of composite single-lap bonded joints, Compos. Struct. 92 (9) (2010) 2194–2202. X. Guo, Z.D. Guan, H.C. Nie, R.M. Tan, Z.S. Li, Damage tolerance analysis of adhesively bonded composite single lap joints containing a debond flaw, J. Adhes. 93 (3) (2017) 216–234. H. Hu, Z. Yang, P. Sarkar, Dynamic wind loads and wake characteristics of a wind turbine model in an atmospheric boundary layer wind, Exp. Fluids 52 (5) (2012) 1277–1294. M.O. Hansen, Aerodynamics of Wind Turbines, Routledge, 2013. L. Germanischer, Guideline for the Certification of Wind Turbines Edition 2010 [G], Germany, (2010). P.S. Veers, T.D. Ashwill, H.J. Sutherland, D.L. Laird, D.W. Lobitz, D.A. Griffin, J.F. Mandell, W.D. Musial, K. Jackson, M. Zuteck, Trends in the design, manufacture and evaluation of wind turbine blades, Wind Energy 6 (3) (2003) 245–259. H. Van Grol, B. Bulder, Reference Procedure to Establish Fatigue Stresses for Large Size Wind Turbines: A State of the Art Report, Volume I: Main Body of the Report and Annexes, Netherlands Energy Research Foundation ECN, Petten, 1994. H. Van Grol, B. Bulder, Reference Procedure to Establish Fatigue Stresses for Large Size Wind Turbines: A State of the Art Report. Volume II. Tables and Figures, Netherlands Energy Research Foundation ECN, Petten, 1994. S. Larwood, W. Musial, G. Freebury, A.G. Beattie, NedWind 25 Blade Testing at NREL for the European Standards Measurement and Testing Program, National Renewable Energy Lab, Golden, CO (US), 2001. T. Svensson, Prediction uncertainties at variable amplitude fatigue, Int. J. Fatigue 19 (93) (1997) 295–302. C.H. Lange, Probabilistic Fatigue Methodology and Wind Turbine Reliability, Stanford University, 1996. M. Matsuishi, T. Endo, Fatigue of metals subjected to varying stress, J. Soc. Mech. Eng., Fukuoka, Japan 68 (2) (1968) 37–40. J. Goodman, Mechanics Applied to Engineering, Longmans, Green, 1918. M.A. Miner, Cumulative damage in fatigue, J. Appl. Mech. 12 (3) (1945) 159–164. X. Li, K. Yang, J. Bai, J. Xu, A method to evaluate the overall performance of the CAS-W1 airfoils for wind turbines, J. Renewable Sustainable Energy 5 (6) (2013) 063118. U.V.R.S. Turaga, C.T. Sun, Improved design for metallic and composite single-lap joints, J. Aircr. 45 (2) (2008) 440–447. M.H. Keegan, D. Nash, M. Stack, Numerical Modelling of Hailstone Impact on the Leading Edge of a Wind Turbine Blade, EWEA Annual Wind Energy Event 2013, (2013). A. Niesłony, Determination of fragments of multiaxial service loading strongly influencing the fatigue of machine components, Mech. Syst. Signal Pr 23 (8) (2009) 2712–2721.
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Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Strain response analysis of adhesively bonded extended composite wind turbine blade suffering unsteady aerodynamic loads
T
⁎
Guangxing Wua,b,c, , Zhiwen Qina,b,c, Lei Zhanga,b,c, Ke Yanga,b,c a b c
Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China Key Laboratory of Wind Energy Utilization, Chinese Academy of Sciences, Beijing 100190, China National Research and Development Center of Wind Turbine Blade, Beijing 100190, China
AR TI CLE I NF O
AB S T R A CT
Keywords: Adhesively bonding technology Extended wind turbine blade Strain response Fatigue damage Unsteady aerodynamic loads
Extending blades of wind turbine in service is the most effective method for increasing energy production. Adhesively bonding technology increases less mass and has simpler operation process, which is more suitable for extending blades in service. But unsteady aerodynamic loads on the blades due to stochastic turbulent inflow may lead to fatigue damage and even failure. This paper presented a study on strain response and fatigue life of adhesively bonded extended composite wind turbine blade suffering unsteady aerodynamic loads. Firstly, a loading method that applies periodic distributed aerodynamic loads on the blade was proposed to accurately simulate the unsteady distributed loads on the real extended blades in service. Secondly, strain response behaviors to unsteady aerodynamic loads and strain distribution behaviors in the adhesively bonded area were revealed. Finally, fatigue damage was predicted with unsteady aerodynamic load spectrums, rainflow cycle-counting algorithm, Goodman diagram and Miner's linear superposition principle. Based on the findings obtained from this study, the feasibility of adhesively bonding technology for extending blade was affirmed and a few potential future directions of study were addressed to reduce the risk of adhesively bonded structures.
1. Introduction Increasing the energy production or reducing the maintenance costs is the main way to improve the economy of wind turbines in service. In the wind turbine system, the blades are one of the most critical components to capture the power from wind. It has been well known that [1] the power output is proportional to swept area and wind speed cubed. Therefore, extending blades is one of the most effective method to harvest more wind energy in low wind speed region. Generally, there are two method to extend the wind turbine blades in service, metal bolt connection [2–4] and adhesively bonded connection [5–7]. Compared with metal bolt connection, adhesively bonded connection method has better fatigue behaviors and simpler operation process, and increases less mass, which is more suitable for the connection of composite shell structures and is discussed in this paper. Wind turbine rotors usually run in the nature atmospheric boundary layer. The stochastic turbulent inflow would induce unsteady aerodynamic loads [8,9], which are the primary source of fatigue loads in flapwise direction. How to make sure that the adhesively bonded extended composite wind turbine blade can endure the long-term unsteady aerodynamic loads? Usually, fatigue testing is conducted to verify a blade's ability to withstand its operating load spectrum over a design life of
⁎
Corresponding author at: Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China. E-mail address: [email protected] (G. Wu).
https://doi.org/10.1016/j.engfailanal.2017.12.009 Received 16 May 2017; Accepted 6 December 2017 Available online 07 December 2017 1350-6307/ © 2017 Elsevier Ltd. All rights reserved.
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20 years [10]. The real operating load spectrum consists of more than 109 stochastic load cycles due to irregular turbulent inflow [11]. So the load spectrum is compressed into an equivalent fatigue load history of 106–107 cycles that can be applied in no more than a few months using linear damage principles [12–14]. The equivalent fatigue loads can be applied with hydraulic actuators or resonant eccentric mass [11] installed at one or several locations along the blade. However, Svensson [15] found that the fatigue load variation is an important source of scatter among material variability and other uncertainties. Lange [16] also found that fatigue reliability to be significantly affected by the type of model chosen for the loads data. The hydraulic actuators or resonant eccentric mass methods can only apply concentrated loads, which are clearly different from the distributed loads induced by flow over blades. The purpose of this work is to understand the structural response and predict fatigue damage of adhesively bonded area for extended blades suffering unsteady aerodynamic loads. An experimental method that the distributed aerodynamic loads are applied with a rotating apparatus to the extended blades was proposed and validated by computational fluid dynamics (CFD) method firstly. Secondly, strain response to pitching angle and rotating speed was analyzed, and then the distribution behaviors in the adhesively bonded area were studied. Finally, fatigue damage of adhesively bonded area for extended blades was predicted with unsteady aerodynamic load spectrums, rainflow cycle-counting algorithm [17], Goodman diagram [18] and Miner's linear superposition principle [19]. 2. Experiment setup It has been known that the turbulent inflow in the nature atmospheric boundary layer would induce unsteady aerodynamic loads. In essence, the unsteady loads are resulted from the time-variant inflow angle and speed. In this experimental investigation, a rotating apparatus was designed and ran with pitch angle and rotating speed changed in a control law to simulate the turbulent inflow conditions and generate periodic aerodynamic loads. An adhesively bonded extended blade with length of 3.5 m was designed, manufactured and tested. 2.1. Rotating experimental apparatus It is high cost to build a horizontal axis rotating apparatus for the same rotor diameter, which needs a tower and more room for the indoor test. A rotorcraft-like apparatus was designed and installed on the foundation of laboratory, as shown in Fig. 1. The weight of total apparatus without blades is about 1450 kg and the height at hub center is 1809 mm. When the 3.5 m length blades are mounted on the hub, rotor diameter will be 7674 mm. Rotating motion is driven by a 22 kW AC motor and a gearbox with ratio of 10.41. The rotating speed can be controlled by a frequency converter, and the rated output speed is 150 rpm. The rotating azimuth angle is recorded by a 12-bit encoder with resolution of 0.088°. Pitching motions of two blades are synchronously driven by a servo motor mounted on the hub with a pair of
Fig. 1. The components of rotating experimental apparatus.
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Fig. 2. Chord distributions of extended blade.
bevel gears. A thrust transducer with range of ± 1000 kg and accuracy of 0.5% F·S. was installed inside of hub and used to measure the thrust induced by rotating motion. A torque transducer with range of ± 500 Nm and accuracy of 0.5% F.S was installed between rotating motor and gearbox and used to measure the torque output of rotating motor. Most of the signals, including pitching angle, rotating azimuth angle, thrust, strains on the blades, are transmitted by a 66-channel slip ring. All the signals are sampled and processed by a Siemens S7-300 PLC module and a controlling program. 2.2. Adhesively bonded extended composite wind turbine blade 2.2.1. Geometric shape The extended blade with total length of 3.5 m comprises original blade and extended tip, as shown in Fig. 2. The original blade locates from z = 0 to 2.0 m, and extended tip locates from z = 1.6 to 3.5 m. The adhesively bonded area is from z = 1.6 to 2.0 m. The sectional shape of blade root is a rectangle with size of 160 mm by 100 mm distributed from z = 0 to 0.2 m. An airfoil, CASW1-400 shown in Fig. 3, was chosen from z = 0.52 to 3.4 m, where only the chord is different. CAS-W1-400 with thickness of 40% is one of the thick and blunt trailing-edge airfoil series designed by the Institute of Engineering Thermophysics, Chinese Academy of Sciences [20]. All of the twist angles along the extended blade are 0°. The blade coordinate is shown in Fig. 3 also. Coordinate origin locates at the intersections of rotating axis and pitching axis. The x-axis is in the rotor plane and points to trailing edge. The y-axis is perpendicular to the rotor plane and points up. The z-axis coincides with pitching axis and points from root to tip, which is not shown in Fig. 3. θ is the pitching angle between rotor plane and chord line, and is positive when the leading edge goes up as Fig. 3. 2.2.2. Structures Lay-up sequence along the blade span is shown in Fig. 4 (a). For the original blade, 4 layers of 750 tri-axial fiber and 3 layers of unidirectional fiber were stacked alternately along the total blade. And the blade root from z = 0 to 1.2 m was reinforced by 13 layers of 750 tri-axial fiber gradually. For the extended tip, only 4 layers of 750 tri-axial fiber and 3 layers of unidirectional fiber were stacked alternately along the total tip. The sectional structure except adhesively bonded area are made up of fiberglass reinforced plastic at suction side and pressure side, and adhesive at leading edge and trailing edge, as shown in Fig. 4 (b). At adhesively bonded area from z = 1.6 to 2.0 m, both pressure side and suction side of extended tip covered on the outer surface of original blade, as shown in Fig. 5. In fact, pressure side and suction side will change to each other at different pitching angle due to aerodynamic effect. However, pressure side represents the lower surface and suction side represents the upper surface at all the pitching angle in this work to avoid the confusion of names. The structural adhesive filled in the interface between original blade and extended tip. An extrusion tool was designed to make sure that the thickness of adhesive is 7 mm ± 1 mm. It is suggested from Turaga's work [21] that covering attachment would lead to about 28% improvement in initial failure strength. So the structural adhesive was 45° beveled at z = 1.6 m and a layer of 750 tri-axial fiber covered on the outer surface of adhesively bonded area. The structural adhesive is named WD3135 and purchased from Shanghai KangDa New Materials Co., Ltd. The material properties are listed in Table 1.
Fig. 3. The airfoil and coordinate used for the extended blade.
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Fig. 4. Lay-up sequence along the blade span (a), sectional structure (b).
Fig. 5. Interior structure at adhesively bonded area, spanwise section (a), chordwise section (b).
Table 1 Material properties.
Ultimate tension strength (Mpa) Ultimate compression strength (Mpa) Tensile modulus (Gpa)
UD fiber
750 Tri-axial fiber
Structural adhesive
850 500 39
320 240 17.8
52 52 4.1
2.3. Strain gauge locations set-up Strain gauges were placed at five spanwise locations of one blade, as shown in Fig. 6 (a). Section S1 locates in the original blade, and section S5 locates in the extended tip. The other three sections, S2, S3, S4, locates in the adhesively bonded area. Four strain gauges were placed in the outer surface of every sections, as shown in Fig. 6 (b). Strain gauges located at leading edge and trailing
Fig. 6. Spanwise locations (a) and chordwise locations (b) of strain gauges.
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Fig. 7. Loads applied on the blade in dynamic test case.
edge were used to monitor the change of edgewise loads, while strain gauges located at pressure side and suction side were used to monitor the change of flatwise loads. All the strain data were sampled and recorded by a strain analysis system of DH3820 with sampling frequency of 100 Hz and minimum resolution of 0.5 με. 2.4. Test cases Two test cases, quasi static case and dynamic case, were conducted in this work. In quasi static case, no pitching motion was driven and the pitching angle was kept the same when the strain values were sampled in the rotating motion. Theoretically, the aerodynamic loads are quasi steady without consider of the ground and wall effect, and the centrifugal force is constant at the same rotating speed. In this case, the mean values of strains were analyzed to investigate the effects of pitching angle and rotating speed. The flow field was validated by computational fluid dynamics (CFD) method. In dynamic case, the blade underwent rotating motion and cyclic pitching motion simultaneously. The aerodynamic loads will form unsteady flapwise moment due to cyclic change of pitching angle, as shown in Fig. 7, and the centrifugal force is almost constant at the same rotating speed. In this case, both the mean value and amplitude of strain response were investigated. The test data were used to analyze the strain distributions at the adhesively bonded area, obtain the fatigue loads, and predict the fatigue damage. 3. Aerodynamic loads analysis and validation by CFD method It has been shown from Li's data [20] that lift coefficient of CAS-W1-400 airfoil increases with the increase of angle of attack from −10° to 20°. One way to apply unsteady aerodynamic loads is to change the angle of attack periodically. Unfortunately, the real angles of attack are not known due to the induced flow by rotor motion according to wind turbine aerodynamic theory [9]. However, pitching angle is indirect related to angle of attack and can be easily controlled by pitching motor. To understand the 3D aerodynamic behaviors of the rotating blades, the CFD flow solver package ANSYS Fluent13.0 was employed to simulate the flow field and aerodynamic behaviors of rotating test. The size of computational geometric field is 10 m by 10 m by 3.65 m, which is same as the real test field. Rotating apparatus was simplified into a cylinder. The absolutely coordinate that cells of rotating apparatus and blades (pink parts) base on is fixed on the rotor, shown in Fig. 8. The interior cells and wall cells (blue parts) base on rotating coordinates and rotating speed is 150 rpm, which is same as test case. Total number of meshes is 6,617,120. The Spalart-Allmaras model was chosen as turbulent model, and the SIMPLE algorithm was chosen for coupling the momentum pressure equations. For spatial
Fig. 8. Computational geometric field and absolute coordinate. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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Fig. 9. Sectional normal force (a) and total force (b) at different pitching angle by CFD method.
discretization, a second-order upwind differencing scheme was applied. The convergence criteria for the residuals were O(10− 5) in magnitude. Sectional normal force is the integral of sectional pressure distributions by length of blade strip. The normal force direction is perpendicular to rotating plane and same as y-axis, and tangential force direction is same as x-axis in Fig. 8. Sectional normal forces increase nonlinearly from root to tip at different pitching angles as shown in Fig. 9 (a). Total forces were obtained by the integral of sectional force. It is shown from Fig. 9 (b) that normal force increases with the increase of pitching angle from −20° to 20°. No significant changes were observed about tangential force. Torque of the rotor was calculated by the measured output torque of the rotating motor and reduction ratio of the gearbox in Fig. 1. Meanwhile, rotor torque can be computed by the integral of aerodynamic force in CFD method. The comparisons of rotor torque between measurement and CFD method are shown in Fig. 10. It is indicated that the changing trends of torque along the pitching angle are almost the same. The minimum torque is observed at pitching angle of 0°. However, the measured torque is larger than numerical result at the same pitching angle. The difference may be from the mechanical losses and simplification of numerical model. Lightweight foam strips were used to visualize the flow track near ground in the rotating test and streamlines of relative velocity over the blade is extracted from the CFD results, as shown in Fig. 11. At pitching angle of − 20°, it has been observed from the foam strips that flow direction near ground points to the rotor center. The same results are revealed from streamlines by CFD method. Air from surroundings is induced to move to rotor center near ground, going up to the rooftop and flowing to the surroundings. The tip vortex flow forms with direction pointing from upper surface of blade to lower surface. It is shown from pressure contour that higher pressure distributes on the upper surface, which results in the negative normal force in Fig. 9. Correspondingly, at pitching angle of 20°, the foam strips that flow direction near ground points from the rotor center to surroundings. The tip vortex flow forms with direction pointing from lower surface of blade to upper surface. Higher pressure distributes on the lower surface, which results in the
Fig. 10. Comparisons of rotor torque between measurement and CFD.
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Fig. 11. Flow field at pitching angle of − 20° (a) and 20° (b).
positive normal force in Fig. 9. It is shown from above results that aerodynamic loads are determined by pitching angle and rotating speed. So periodic aerodynamic loads will be applied on the blades when pitching angle is changed circularly. The method is used to simulate unsteady aerodynamic load and investigate the dynamic strain response and fatigue damage of adhesively bonded extended blade. 4. Strain response 4.1. Effects of pitching angle on the mean strain in quasi static test case The strain responses to pitching angles were investigated firstly in quasi static test case. Time history of all the strains at different locations was recorded at rotating speed of 150 rpm. At every pitching angle, the mean strain value of time history was calculated and compared with each other. It is shown from Fig. 12 that with the increase of pitching angle from − 20° to 20°, the strain values at pressure side of different spanwise locations increase and the strain values at suction side decrease approximately linearly. The changes of strain values at leading edge and trailing edge are not obvious at different pitching angles. The results are consistent with the results in Fig. 9. The increase of lift will lead to the increase of flapwise moment, so strain value at pressure side will increase and strain value at suction side will decrease, as shown in Fig. 12. Besides the aerodynamic force, the blade suffers centrifugal force in the rotating motion. The aerodynamic force varies with pitching angle at the same rotating speed, while centrifugal force is almost constant. All the strain values are positive in Fig. 12, which means only the tension deflection acts on the blade. Therefore, at the pitching angle of − 20°, strain value of pressure side is positive but lower than strain value of suction side, as shown in Fig. 13. At the pitching angle of 20°, strain value of suction side is positive but lower than strain value of pressure side. 4.2. Effects of rotating speed on the mean strain values in quasi static test case It has been well known that the aerodynamic force and centrifugal force are both proportional to the square of rotor speed, as shown in the Eq. (1), where dL is the lift of blade strip; Cl is the lift coefficient; ρ is the density of air; ω is the rotor speed; dS is the area of blade strip; r is spanwise distance from rotor center; dC is the centrifugal force; dm is the mass of blade strip. 1
1
⎧ dL = Cl⋅ 2 ρv 2⋅dS = ω2⋅ 2 Cl ρr 2dS ⎨ dC = ω2r⋅dm ⎩
(1) 42
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Fig. 12. The effects of pitching angle on the mean strain values at different locations.
Fig. 13. Load analysis at different pitching angles.
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Fig. 14. The effects of rotating speed on the mean strain values and the fit curve.
So the strain value and rotor speed should present quadratic function relation. Pressure side of section S1 with maximum strain in the measured area and pressure side of section S4 with maximum strain in adhesively bonded area are focused in this section. The measured strain values at pressure side of sections S1 and S4 at pitching angle of 0° are shown by scatter in Fig. 14. The corresponding curves were fitted by quadratic polynomials. For section S1, the expression of fit curve is (2)
ε = 7.39233 + 0.77627Ω + 0.01059Ω2 with correlation coefficient of 0.99926. For section S4, the expression of fit curve is
(3)
ε = 17.49317 + 0.47674Ω + 0.00541Ω2 with correlation coefficient of 0.9997. 4.3. Time history analysis on the strain in dynamic test case
In dynamic test case, pitching angle was driven to change from − 20° to 20° with speed of 80°/s continuously, while rotating speed is 150 rpm. Time history of strain at pressure side of section S1 is shown in Fig. 15 by blue curve, and red curve represents pitching angle. The variation of strain is in tune with pitching angle, though more slight oscillations in variation of strain and phase offset show the complexity of dynamic strain response. The FFT (fast Fourier transform) algorithm is used to investigate the frequency components of strain time history in Fig. 15. It is shown in Fig. 16 (a) that strain response includes three higher-amplitude oscillations with frequency of 0.92 Hz, 2.497 Hz and 4.94 Hz. Compared with the pitching frequency of 1.1 Hz, rotating frequency 2.5 Hz, and first-order flapwise natural frequency of 5.3 Hz, the three higher-amplitude oscillations are directly related to pitching motion, rotating motion and first-order flapwise modal.
Fig. 15. Time history of strain at section S1 in cyclic pitching motion.
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Fig. 16. Frequency analysis by FFT, (a) frequency domain character, (b) bond pass filter.
There are also some high-frequency and low-amplitude oscillations. A bond pass filter from 0.5 to 5 Hz was applied to time history in Fig. 15. It is shown from Fig. 16 (b) that the strain time histories before and after the filter are almost the same, which means that the three higher-amplitude oscillations play a dominant role. 5. Strain distributions in the adhesively bonded area In dynamic test case, flapwise load varies periodically with the cyclic pitching motion. Therefore, strains at pressure side and suction side in different spanwise sections were focused to investigate the strain distributions. The average and standard deviation of strain oscillation in dynamic test case with pitching speed of 80°/s and rotating speed is 150 rpm were computed and compared. It is shown from Fig. 17 (a) that the average strain of pressure side is largest at section S1, and is smallest at section S2. The average strain increases gradually from section S2 to S5. The same variation was observed on the strains of standard deviation. At suction side, only strains at three sections from S2 to S4 were measured. The average strain increases gradually from section S2 to S4 in Fig. 17 (b), which is same as the variation of strains at pressure side. The adhesively bonded structure was considered to analyze the strain distributions in Fig. 17. It is shown in Fig. 18 that sections from S2 to S4 are in the adhesively bonded area, where the stiffness is larger than sections S1 and S5. So the strains of sections from S2 to S4 are smaller than strains of sections S1 and S5. Meanwhile, the outer surface of section S2 is close to the free end, where the local stress is minimum. Hence, the strain increases gradually from section S2 to S4 and the strain of section S2 is smallest. It is well known that the load will accumulate from blade tip to root. The load at section S5 is lower than section S1, which induces that the strain of section S5 is smaller. All the above influence factors result in the strain distributions in Fig. 17. 6. Evaluation of fatigue damage The strain at pressure side of section S4 is largest in the adhesively bonded area, and the strain at pressure side of section S1 is largest in the measuring area. In this work, the dynamic strain response at pressure side of section S4 was focused to investigate the fatigue damage of structural adhesive. The dynamic strain response at pressure side of section S1 was focused to investigate the fatigue damage of UD fiber and 750 tri-axial fiber. In the dynamic test case, the maximum rotating speed is 150 rpm, so the corresponding tip speed is 54.98 m/s. It has been summarized from Keegan's work [22] that tip speeds of wind turbine in excess of 80 m/s are now common, with many actually
Fig. 17. Strain distributions at pressure side (a) and suction side (b).
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Fig. 18. Strain distribution analysis.
exhibiting tip speeds of about 90 m/s and some select designs exceeding 100 m/s. Hence, in order to evaluate the fatigue damage of actual extended blade, the measured dynamic strain responses are needed to extrapolate from the tested tip speed to actual tip speed firstly to produce the fatigue strain spectrum. Then mean value and amplitude were counted by a cycle-counting algorithm, so-called Rainflow analysis [23]. A Goodman diagram in the guideline [10] was used to account for the effect of mean strain on the material fatigue damage and the number of tolerable load cycles was obtained by the ultimate strength. Finally, the Miner's linear superposition rule [19] was used to determine the fatigue damage. 6.1. Extrapolations of fatigue load spectrum The tested tip speed of the extended blade is 54.98 m/s, while the actual tip speed of wind turbine in rated wind speed is about 90 m/s. The measured dynamic strain response should be extrapolated from tested tip speed to actual tip speed. Firstly, rotating speed is transformed by the actual tip speed of 90 m/s with the Eq. (4), where Ω is the rotating speed, v is the tip speed, R is the distance between blade tip and rotating center.
Ω= vR
(4)
Fig. 19. Comparison of extrapolated and measured strain spectrum, (a) section S1, (b) section S4.
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Fig. 20. Rainflow cycle counting for extrapolated strain spectrum of section S1 (a) and section S4 (b).
The mean value of strain of sections S1 and S4 at the actual tip speed can be obtained by Eqs. (2) and (3), respectively. Then the multiple between the mean strain at actual tip speed and at the tested tip speed can be calculated. The multiple is 2.310 for strain of section S1, and 2.187 for strain of section S4. Finally, the extrapolated strain spectrum is the measured strain spectrum by the multiples. The comparison of extrapolated strain spectrum and measured strain spectrum is shown in Fig. 19. 6.2. Rainflow analysis The rainflow cycle counting algorithm used in this work is from a MATLAB code, which has been officially presented and described in Niesłony's work [23]. The algorithm is widely used while fatigue life assessment of structures under non-constant amplitude loading. Usually, the algorithm extract cycles from load, stress or strain history obtained from measurement or simulation. As a results of the counting several cycles and half-cycles with different amplitude and mean value are obtained. The extrapolated dynamic strain spectrums in Fig. 19 were analyzed by the rainflow cycle counting MATLAB code. The threedimensional histograms were obtained and have shown the number of cycles present in the strain spectrums of 3 min associated with a combination of the strain amplitude and the strain mean value in Fig. 20. 6.3. Fatigue damage evaluation Firstly, the stress is calculated by the Eq. (5), where σ is the stress, E is the modulus shown in Table 1, ε is the strain. (5)
σ = Eε
Then the number of tolerable load cycles at the mean value and amplitude of strain in rainflow results can be determined with the Eq. (6) in the guideline for the certification of wind turbines [10] as follows: m
Rk, t + |Rk,c| − |2⋅γMa⋅Sk, M − Rk, t + |Rk, c || ⎤ N=⎡ ⎢ ⎥ 2⋅(γMb/ C1b)⋅Sk,A ⎣ ⎦
(6)
where, Sk, M is the mean value of stress history, Sk, A is the amplitude of stress history, Rk, t is the ultimate tension strength in Table 1, Rk, c is the ultimate compression strength in Table 1, m is the slope parameter of S/N curve and is 10 for laminates with epoxy resin matrix, N is the permissible load cycle number, γMa is the partial safety factor for short-term strength of the material, γMb/C1b is the partial safety factor for fatigue strength of the material. In this work, γMa is equal to 1.35 × 1.35 × 1.1 × 1.2 × 1.1 for UD fiber and 750 tri-axial fiber and 1.35 for adhesive.γMb/C1b is equal to 1.35 × 1.1 × 1 × 1 × 1.1 for UD fiber, 1.35 × 1.1 × 1.2 × 1 × 1.1 for 750 tri-axial fiber, and 1.35 × 1 × 1.1 × 1.1 × 1.1 for adhesive. The values of γMa and γMb/C1bare determined by the description in detailed in the guideline. The number of tolerable load cycles at different amplitudes of strain oscillations are shown in Fig. 21. With the same strain amplitudes, UD fiber presents better fatigue behavior and adhesive presents worst fatigue behavior. To evaluate the fatigue damage of different materials under the unsteady aerodynamic loads, the Miner's linear superposition rule [19] was used to determine the accumulated fatigue damage in 20 years. The fatigue damage D is defined as the sum of the quotients of existing load cycle numbers ni to permissible load cycle numbers Ni, as shown in Eq. (7).
D=
n
∑ Ni i
(7)
i
It will be safe when the accumulated fatigue damage of all the materials in the extended blade is less than 1. The accumulated fatigue damages in 20 years for the three materials are shown in Table 2. All the damages are much less than 1. However, under the tested unsteady aerodynamic loads, 750 tri-axial fiber will suffer more damage and adhesive will suffer less damage, which means 47
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Fig. 21. The S/N curve results of different materials.
Table 2 Accumulated fatigue damages in 20 years.
Fatigue damage
UD fiber
750 tri-axial fiber
Structural adhesive
1.67 × 10− 5
9.21 × 10− 5
2.07 × 10− 7
that the adhesively bonded area is not the most dangerous location. It is shown that the tensile fatigue behaviors of adhesively bonded extended blade has been analyzed in this work. However, the shear strain of adhesive, which is also an important deformation type, is not measured in this test. The fatigue behavior of shear deformation in the adhesive should be investigated in the further work.
7. Conclusions An adhesively bonded extended blade was manufactured and an experimental method that the periodic aerodynamic loads are applied with a rotating and pitching apparatus was conducted to understand the structural response and predict fatigue damage of adhesively bonded extended blades. The conclusions are summarized as follows: 1) Periodic aerodynamic loads will be applied on the blades when pitching angle is changed circularly. Normal force increases with the increase of pitching angle from − 20° to 20°. No significant changes were observed about tangential force. At pitching angle of − 20°, Air from surroundings is induced to move to rotor center near ground, going up to the rooftop and flowing to the surroundings. The tip vortex flow forms with direction pointing from upper surface of blade to lower surface. The flow direction is opposite when the pitching angle is 20°. 2) With the increase of pitching angle from − 20° to 20°, the strain values at pressure side increase and the strain values at suction side decrease approximately linearly. The changes of strain values at leading edge and trailing edge are not obvious at different pitching angles. The strain value and rotating speed present quadratic function relation. The strain oscillations due to pitching motion, rotating motion and first-order flapwise modal play the dominant role in the dynamic strain response. 3) The free end, larger stiffness in adhesively bonded area and load accumulation from blade tip to root result in the strain distributions along the blade span. 4) All the materials used in the extended blade, UD fiber, 750 tri-axial fiber and structural adhesive, are safe enough in the design life of 20 years and the adhesively bonded area is not the most dangerous location. The fatigue behavior of shear deformation in the adhesive should be investigated in the further work.
Acknowledgments The project is supported by the National Natural Science Fund Youth Foundation of China (51706228), and the Research Equipment Development Project of Chinese Academy of Sciences (YZ201513).
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