METHOD FOR QUICKLY PREDICTING FATIGUE LIFE OF WRINKLE DEFECT-CONTAINING MAIN SPAR IN WIND TURBINE BLADE

Abstract

A method for quickly predicting a fatigue life of a wrinkle defect-containing main spar in a wind turbine blade is provided. The method includes: S1: testing a tensile property of a wrinkle defect-containing main spar to be tested; S2: calculating, according to surface temperature data of the specimen obtained in step S1, intrinsic dissipated energy of the main spar specimen under different loading stresses; S3: plotting a relational graph between intrinsic dissipated energy of the specimen and a corresponding ultimate tensile strength (UTS) level; S4: establishing, based on a change of the intrinsic dissipated energy in a fatigue process, a normalized residual stiffness model containing parameters to be determined, and putting fatigue test data into the model; S5: deducing a fatigue life prediction model for the wrinkle defect-containing main spar specimen according to the normalized residual stiffness model with determined parameters; and S6: obtaining a normalized failure stiffness.

Claims

1. A method for quickly predicting a fatigue life of a wrinkle defect-containing main spar in a wind turbine blade, comprising: step S1: testing, on a universal fatigue testing machine, a tensile property of a wrinkle defect-containing main spar specimen to be tested, to obtain an ultimate tensile strength (UTS); and synchronously monitoring and recording a temperature change on a surface of the specimen with an infrared thermal imager during a fatigue test, and counting and recording surface temperature, stress, strain and stiffness data of the specimen under different numbers of cycles upon completion of the test; step S2: calculating, according to surface temperature data of the specimen obtained in step S1, intrinsic dissipated energy of the main spar specimen under different loading stresses in a temperature stabilizing stage; step S3: plotting a relational graph between intrinsic dissipated energy d.sub.ista of the specimen and a corresponding UTS level, performing interpolation with two curve method on data trendlines having two different slopes in the relational graph, and determining a fatigue limit of the specimen according to a σ.sub.max coordinate value of an intersection of two straight lines, wherein an area with a load above the fatigue limit is considered as an overloaded area, which is an area where a failure of the specimen occurs; and there is no failure of the specimen in an area with a load below the fatigue limit during the test; step S4: establishing, based on a change of intrinsic dissipated energy in a fatigue process, a normalized residual stiffness model containing parameters to be determined, and putting fatigue test data recorded in steps S1 and S2 into the model to determine values of unknown parameters a, b, p and q in the model, wherein a and b are parameters related to a wrinkle defect in a material; and p and q are two material parameters independent of the intrinsic dissipated energy and a loading cycle; step S5: deducing a fatigue life prediction model for the wrinkle defect-containing main spar specimen according to the normalized residual stiffness model with the determined parameters; and step S6: defining a number of cycles under which the specimen sustains a maximum fatigue load to determine a normalized failure stiffness; and predicting, through the fatigue life prediction model with the determined normalized failure stiffness, the fatigue life of the specimen to be tested, in the overloaded area to obtain a predicted S-N curve of the wrinkle defect-containing main spar specimen.

2. The method of claim 1, wherein in step S1, a maximum loading stress of the fatigue test is applied to the specimen at a step size of 5% in a range of 20%-90% of the UTS; and each time, the specimen is only tested within 8,000 loading cycles.

3. The method of claim 1, wherein the universal fatigue testing machine in step S1 is a MTS810 hydraulic electromagnetic servo fatigue machine; the tensile property is tested at a displacement rate of 2 mm/min; and the specimen is subjected to a constant tensile loading amplitude sinusoidal wave form with a frequency of 10 Hz and a stress ratio of 0.1.

4. The method of claim 1, wherein calculating the intrinsic dissipated energy of the main spar specimen in the temperature stabilizing stage in step S2 comprises: ignoring, when a uniform uniaxial cyclic load is applied to the main spar, an internal coupling source between an internal variable and a temperature; and implementing a balance between heat loss and the intrinsic dissipated energy when each cycle of the specimen is ended in the temperature stabilizing stage of the fatigue process, and expressing a model for calculating a stable intrinsic dissipated energy in the stage as:
d.sub.istab=−div(kgradT.sub.stab)  (1) wherein, T.sub.stab is a temperature of the specimen in a surface temperature stabilizing stage in units of ° C., k is a thermal conductivity in units of W/(m.Math.K), and div(kgradT.sub.stab) is a heat loss rate arising from heat conduction.

5. The method of claim 1, wherein establishing the normalized residual stiffness model in step S4 comprises: step S41: expressing a fatigue damage indicator D(n) during the fatigue test with a residual stiffness under the fatigue load as: $\begin{array}{cc}D\left(n\right)=\frac{E_0-E\left(n\right)}{E_0-E_f}=\frac{1-E^{\prime }\left(n\right)}{1-E_f^{\prime }}& \left(2\right)\end{array}$ wherein, n is a number of cycles; E(n) is a stiffness corresponding to an nth cycle; E.sub.0 is an initial effective stiffness along an x-axis direction; E′(n) is a normalized residual stiffness corresponding to the nth cycle, and is defined as E(n)/E.sub.0; E.sub.f is a failure stiffness; and E′.sub.f is a normalized failure stiffness at a final cycle N.sub.f, and is defined as E.sub.f/E.sub.0; and step S42: establishing a relational expression between a normalized residual stiffness E′(n) in a fatigue-loading x-axis direction and the number of cycles as follows by introducing an influence of a height-width ratio in the wrinkle defect, based on a fact that a certain relation is present between a stable intrinsic dissipated energy value d.sub.istab and a damage accumulation: $\begin{array}{cc}{E}^{\prime }\left(n\right)=\frac{1}{{a\left(A/L\right)}^b+1}\left(1-{\mathrm{pd}}_{\mathrm{istab}}{n}^{1/q}\right)& \left(3\right)\end{array}$ wherein, A and L are respectively a height and a width of an out-of-plane wrinkle defect; a and b are the parameters related to the wrinkle defect in the material; p and q are two material parameters independent of the intrinsic dissipated energy and the loading cycle; the normalized residual stiffness E′(n) is dimensionless, p is denoted in units of /(J.Math.m.sup.−3.Math.s.sup.−1).sup.−1 and a, b and q are defined as dimensionless parameters for keeping a dimension uniform; the parameters a and b are used to reflect an influence from a geometry of the wrinkle; the parameter q is used to control a shape of a function; and parameter p is used to regulate an influence of d.sub.istab, considering that d.sub.istab in the fatigue process depends on a test material.

6. The method of claim 1, wherein establishing the fatigue life prediction model in step S5 comprises: step S51: expressing, in combination with the equation (2) and the equation (3), the fatigue damage indicator as: $\begin{array}{cc}D\left(n\right)=\frac{1\frac{1-{\mathrm{pd}}_{\mathrm{istab}}{n}^{1/q}}{{a\left(A/L\right)}^b+1}}{1-E_f^{\prime }}& \left(4\right)\end{array}$ step S52: implementing an effect that a damage accumulation indicator must be 1 in a case of the final cycle N.sub.f to failure, which is expressed as D(N.sub.f)=1, and expressing the deduced fatigue life prediction model as: $\begin{array}{cc}{N}_f={\left\{\frac{1-\left[{a\left(A/L\right)}^b+1\right]\left(1-E_f^{\prime }\right)}{p{d}_{\mathrm{istab}}}\right\}}^q& \left(5\right)\end{array}$

7. The method of claim 1, wherein a selected main spar to be tested in the wind turbine blade is made of unidirectional glass fiber reinforced polymer (GFRP) material.

8. The method of claim 1, wherein a predicted fatigue life result is obtained with a conventional fatigue test, or is also estimated with the proposed life prediction model.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The present disclosure will be further described below with reference to the drawings and specific embodiments. The protection scope of the present disclosure is not limited to the following descriptions.

[0033] In the drawings:

[0034] FIG. 1 shows a flow chart of an embodiment of a method for predicting a fatigue life according to the present disclosure;

[0035] FIG. 2 shows a surface temperature change curve according to an embodiment of the present disclosure;

[0036] FIG. 3 shows a relational graph between a maximum loading stress σ.sub.max and intrinsic dissipated energy d.sub.istab according to an embodiment of the present disclosure;

[0037] FIG. 4 shows a three-dimensional (3D) data graph among the number n of cycles, a normalized residual stiffness E′(n) and the intrinsic dissipated energy d.sub.istab according to an embodiment of the present disclosure; and

[0038] FIG. 5 shows a result of a predicted S-N curve of a fatigue test and a fatigue life result of a conventional test according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0039] In order to make the technical problems, technical solutions, and beneficial effects solved by the present disclosure clearer, the present disclosure will be further described below in detail with reference to the drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely intended to explain rather than limit the present disclosure.

[0040] FIG. 1 shows a flow chart of a method for predicting a fatigue life according to the present disclosure. The method includes steps 1-6.

[0041] In step 1, a wrinkle defect-containing main spar specimen is tested for tensile properties on a universal fatigue testing machine to obtain an ultimate tensile strength (UTS). A maximum loading stress of a fatigue test is applied to the specimen at a step size of 5% in a range of 20%-90% of the UTS, and each time, the specimen is tested only within 8,000 loading cycles. And a temperature change on a surface of the specimen is synchronously observed and recorded with an infrared thermal imager during the fatigue test to obtain test data related to a fatigue life.

[0042] In step 2, according to the surface temperature data of the specimen obtained in step S1, intrinsic dissipated energy of the main spar specimen in a temperature stabilizing stage under different loading stresses is calculated.

[0043] In step 3, a relational graph between intrinsic dissipated energy d.sub.ista of the specimen and a corresponding UTS level is plotted, interpolation is performed with two curve method on data trendlines having two different slopes in the relational graph, and a fatigue limit of the specimen is determined according to a σ.sub.max coordinate value of an intersection of two straight lines. An area with a load above the fatigue limit is considered as an overloaded area, namely, an area where a failure of the specimen occurs; and there is no failure of the specimen in an area with a load below the fatigue limit during the test.

[0044] In step 4, a normalized residual stiffness model containing parameters to be determined is established based on a change of intrinsic dissipated energy in a fatigue process. The fatigue test data recorded in steps 1 and 2 is put into the model to determine related parameter values in the model.

[0045] In step 5, for the wrinkle defect-containing main spar specimen, a fatigue life prediction model is deduced according to the normalized residual stiffness model with the determined parameters.

[0046] In step 6, the number of cycles under which the specimen may sustain a maximum fatigue load is defined as 10.sup.6 cycles to obtain a normalized failure stiffness. The fatigue life prediction of the specimen to be tested in the overloaded area is performed through the fatigue life prediction model with the determined normalized failure stiffness to obtain a predicted S-N curve of the wrinkle defect-containing main spar specimen.

[0047] In an embodiment, materials used by the specimen are selected from actual large blade fabrication companies, for example, the materials include the 1250 gsm glass fiber fabricated by the PPG-Devold and the 135 epoxy resin fabricated by the Hexion RIM. In the embodiment, a laminate specimen structurally identical with an actual main spar and including 10 unidirectional overlays is fabricated. The laminate specimen has a dimension of 255 mm (length)×30 mm (width)×10 mm (thickness). When the laminate specimen is fabricated, a cylindrical plastic rod is inserted into a center of a bottom fiber cloth before vacuum pumping, so as to introduce the wrinkle defect. The laminate specimen in the embodiment has a height-width ratio of 0.4 and contains the wrinkle defect in the center. Performance parameters of the glass fiber and the epoxy resin have been known from a supplier data sheet. Table 1 shows elastic parameters of these materials. Table 2 shows geometric features of the specimen.

TABLE-US-00001 TABLE 1 Elastic properties of the materials E.sub.11(Gpa) E.sub.22(Gpa) E.sub.33(Gpa) G.sub.12(Gpa) G.sub.13(Gpa) G.sub.2(Gpa) ν.sub.12 ν.sub.13 ν.sub.23 Glass 7.51 1.24 1.27 2.53 1.93 1.4 0.24 0.34 0.26 fiber Epoxy 3.52 1.44 0.32 resin

TABLE-US-00002 TABLE 2 Geometric features of the wrinkle defect-containing specimen Misplacement angle of the wrinkling Height Width fiber θ(°) A (mm) L (mm) A/L 39 1.8 4.5 0.4

[0048] The fatigue testing machine is a hydraulic electromagnetic servo fatigue machine (MTS 810). The tensile property of the specimen is tested first, where a displacement rate is 2 mm/min. The test is performed till the specimen is ruptured, and it is determined that the UTS and the ultimate tensile strain of the specimen are respectively 0.92 GPa and 0.1625 mm. The specimen is then subjected to a constant tensile loading amplitude sinusoidal wave form with a frequency of 10 Hz and a stress ratio of 0.1. In the embodiment, the applied maximum loading stress varies between 20% and 90% of the UTS at an interval of 5%. For each maximum loading stress, the specimen is only tested within 8,000 loading cycles, it is not necessary to perform the fatigue test on the specimen till the failure of the specimen, and the relation curve between the maximum loading stress σ.sub.max and the stable intrinsic dissipated energy d.sub.istab may be obtained. During the test, the infrared thermal imager is used to monitor and record the temperature on the surface of the specimen and is 400 mm away from the surface of the specimen. Meanwhile, strain gauges adhered on two ends of the specimen are used to measure a strain in the loading direction of the specimen to obtain the residual stiffness.

[0049] Under different maximum loading stresses, the average temperature change on the surface of the specimen recorded by the infrared thermal imager is shown in FIG. 2. The stable surface temperature data T of the specimen in the II stage under each stress is put into following intrinsic dissipated energy calculation expression:

d.sub.istab=−div(kgradT)  (1)

[0050] where, k is a thermal conductivity, and k=1.5 W/(m.Math.k). A relationship between the maximum loading stress σ.sub.max and the intrinsic dissipated energy d.sub.istab is obtained through the calculation of Equation (1), as shown in FIG. 3.

[0051] FIG. 3 shows that the data has linear trends with two different slopes. Through linear fitting with a least square method, two straight lines below and above the fatigue limit are determined. The horizontal coordinate of a data intersection of the two linear regression lines corresponds to the fatigue limit of the specimen. According to FIG. 3, the fatigue limit of the specimen may be determined as 80.8% of UTS.

[0052] In the present disclosure, the load above the fatigue limit is considered as the overloaded area, namely, the area where the failure of the specimen occurs, there is no failure of the specimen when the load is below the fatigue limit, and thus the prediction is only performed to the fatigue life in the failure area. The method for determining the fatigue limit in the present disclosure only needs to acquire the average stable temperature rise of the specimen within 8,000 cycles under different loading stresses, which overcomes the limitation that the conventional fatigue method require a number of specimens and long test time.

[0053] A relational expression between the normalized residual stiffness in the fatigue-loading direction and the number of cycles is established as:

[00005]$\begin{array}{cc}{E}^{\prime }\left(n\right)=\frac{1}{{a\left(A/L\right)}^b+1}\left(1-{\mathrm{pd}}_{\mathrm{istab}}{n}^{1/q}\right)& \left(2\right)\end{array}$

[0054] The geometric parameter A/L=0.4 of the specimen and the d.sub.istab and E′(n) data under different numbers n of cycles in FIG. 4 are put into Equation (2) to obtain parameter values of a, b, p and q. Four unknown parameter values, specifically a=−5.31034, b=5.09028, p=0.00336 and q=−2.18267E17, may be obtained. The determined parameter values are put into Equation (2). Owing to the number n=10.sup.6 of cycles to failure corresponding to the fatigue limit, d.sub.istab=41.3 kJ/m.sup.3. According to Equation (2), the normalized stiffness E′.sub.f=0.624 in the failure of the specimen is obtained.

[0055] The fatigue life prediction model has the following expression:

[00006]$\begin{array}{cc}{N}_f={\left\{\frac{1-\left[{a\left(A/L\right)}^b+1\right]\left(1-E_f^{\prime }\right)}{p{d}_{\mathrm{istab}}}\right\}}^q& \left(3\right)\end{array}$

[0056] After a, b, p, q and E′.sub.f are known, the d.sub.istab under different stresses may be put into Equation (3) to predict a whole S-N curve of the specimen. The S-N curve predicted in the fatigue test in the embodiment of the present disclosure is shown in FIG. 5.

[0057] The S-N curve of the specimen may be predicted with the proposed life prediction model, and may also be obtained with a conventional fatigue test. In the embodiment, the conventional fatigue test is also performed on the specimen by respectively applying five maximum stresses, namely 95%, 90%, 85%, 80% and 75% of the UTS, to load each maximum stress under the control of the load till the failure of the specimen or an end of 10.sup.6 cycles. FIG. 5 shows the result of the conventional fatigue test of the specimen. The predicted S-N curve fits well with the life results of the conventional test; and the predicted life results are within a 95% confidence interval of the conventional results, and comply with the general authentication rule of the wind turbine blade. The S-N curve predicted under the 10.sup.6 cycles to failure in the present disclosure is not overestimated, and predicted results are basically less than the conventional test results, which is relatively conservative and meets the safety considerations in actual engineering.

[0058] It should be noted that the above specific descriptions on the present disclosure are merely for illustrating the present disclosure and are not limited to the technical solutions described in the embodiments of the present disclosure. A person of ordinary skill in the art should understand that the technical solutions of the present disclosure may be modified or equivalently replaced to achieve the same technical effects. These modifications or equivalent replacements shall all fall within the protection scope of the present disclosure as long as meeting the use requirements.