- Email: [email protected]
Investigation of fatigue life for a medium scale composite wind turbine blade
International Journalof Fatigue
International Journal of Fatigue 28 (2006) 1382–1388
www.elsevier.com/locate/ijfatigue
Investigation of fatigue life for a medium scale composite wind turbine blade Changduk Kong
a,*
, Taekhyun Kim a, Dongju Han b, Yoshihiko Sugiyama
c
a Department of Aerospace Engineering, Chosun University, #375 Seosuk-dong, Kwangju, Republic of Korea Sunaerosys Inc., Research Institute, #248-1, Songwon-ri, Nam-myun, Yunki-gun, Chung-Nam, Republic of Korea Department of Mechanical and System Engineering, Ryukoku University, 67 Tsukamoto-cho, Fukakusa Fushimi-ku, Kyoto, Japan b
c
Available online 23 March 2006
Abstract In order to satisfy fatigue requirements in designing a cost effective wind turbine, the wind turbine blade, which is an expensive key component of the wind turbine system, must achieve very long operating life of 20–30 years. In this study, the fatigue life of a medium scale (750 kW) horizontal axis wind turbine system (HAWIS), which has been developed by the present study, was estimated by using the well-known S–N damage equation, the load spectrum and Spera’s empirical formulae in order to confirm more than 20 years operating life. A specific fatigue procedure was proposed with the following three steps. Firstly, from the sample load spectrum data during short period operation, the spectrum data were rearranged as layer numbers, wind speeds, cycles per layer, normalized maximum, minimum, cyclic and average loads, and stress ratios in time order, and then the rearranged data were recorded as cyclic loads per median cyclic load, cycles per layer, cumulative cycles, probability of exceeding, and types of cycles, such as Type I, II and III. Secondly, fatigue loads, such as flapwise and chordwise bending moments were calculated by Spera’s empirical equations with various engineering data of the studying blade for probability of exceeding. Finally, the allowable fatigue strengths were determined from laboratory fatigue property data for the S–N curve of E-glass/epoxy obtained by Mandell, empirical coefficients derived by Goodman diagram with the modified stress ratio and the required design life. In prediction of the fatigue life, it was confirmed that the composite wind turbine blade satisfies the design criteria for the 20 years fatigue life because of sufficient safety margins from the fatigue requirement. 2006 Elsevier Ltd. All rights reserved. Keywords: Composite wind turbine blade; Fatigue life; S–N damage equation; Spera’s empirical equations
1. Introduction The fast progress in wind energy technology and wide spread usage of wind turbines require a standardization of the wind turbine main components aiming at a further cost reduction. This is related not only to large volume production and standardization of production methods but also to material test methods and design rules [1,2]. In South Korea, since the introduction of the ‘‘New and Renewable Source of Energy (NRSE) Development & Promotion Act’’ in 1987, the Korean government has invested *
Corresponding author. Tel./fax: +82 62 230 7188. E-mail address: [email protected] (C. Kong).
0142-1123/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2006.02.034
considerably on the development of a new wind turbine system. One of these initiatives resulted in the design and manufacturing of an E-glass/epoxy composite blade for a 750 kW medium-scale horizontal axis wind turbine system (HAWTS) [3]. The first author and his co-workers have contributed considerably to the structural design and analysis, manufacturing and structural testing of this medium scale composite blade [4–9]. This study developed specific structural design and test procedure for the medium scale E-glass/epoxy composite wind turbine blade through performing aerodynamic design, dynamic and static load analyses, structural design, securing structural strength by static structural analysis, prediction of fatigue life from the random load spectrum,
C. Kong et al. / International Journal of Fatigue 28 (2006) 1382–1388
the modal analysis to prevent the resonance, the structural test with specific test rigs, fixtures and measuring equipments, etc. Furthermore, this study describes a specific blade root joint with inserted bolts and a specific structural configuration, such as the cell box type using the skin-spar-foam sandwich structure not only to minimize the blade weight but also to obtain the structural stability against buckling and vibrating. Among design activities, the cost effective design of the wind turbine structure is one of the most important design works. In order to meet this condition, the wind turbine blade, which is one of the major components of the wind turbine system, must meet the fatigue life requirement of 20–30 years. Fatigue life is usually expressed by term of cycles of failure, which is the number of repetitions of significant loads that can be sustained until initiation and propagation of cracks to an allowable length. Generally the curve of allowable cyclic stress against the number of cycles of failure is called as the S–N curve. Fatigue life is very sensitive to the amplitude of stress variations. In order to account the stress spectrum effect successively, there are two general methods, such as the S–N linear damage and the fracture-mechanics methods [10]. The linear damage hypothesis, which is one of the simplest methods of the accumulation of fatigue damage during reported cycles of stress, was proposed by Palmgren [11] and Miner [12]. According to this hypothesis, if the stress cycle remains constant throughout a fatigue lifetime equal to N, then the fraction of that lifetime consumed on every cycle is constant and equal to 1/N. This fracture is also defined as the damage per cycle, and the total damage at failure is equal to unity. A fracture-mechanics model with the fatigue damage process is more complex than the S–N linear damage model. But many fatigue specialists considers that the most representative model of the physical processes leading to fatigue failure is the fracture-mechanics model. The fracture-mechanics analysis is a validated tool in structural engineering, and the application of this tool for the wind turbine design is straightforward. Fatigue design methodology, experience and verification by field tests are much more critical to success [10]. A fundamental concept of the fracture-mechanics method is that all structures contain small flaws when they are first placed in service. The size of these pre-existed or initial flaws is related to the inspection methods used and the specified acceptance criteria. Flaws in critical areas develop into cracks when fatigue loads are applied, and these cracks continue to grow in length or propagate during in service life of the structure. Crack length is the measure of fatigue damage, and the crack propagation rate is a highly non-linear function of crack length and elapsed time. At the start of service, crack lengths and crack propagation rates are very low. As the crack grows the propagation rate accelerates. Eventually a crack length is
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Fig. 1. Fatigue design procedure of medium scale composite wind turbine blade.
reached that is unstable, the propagation rate becomes infinite, and fracture occurs. In this study, a specific fatigue design procedure is proposed as show in Fig. 1. This fatigue design procedure is based on the previous studies, such as the statistical analysis of fatigue loads and stress spectra, calculation of fatigue loads by Spera’s empirical formulae and estimation for the fatigue allowable strength by the S–N linear damage method proposed by Palmgren and Miner [10–12]. 2. Design summary of the composite wind turbine blade Prior to discussion on the fatigue life of the composite wind turbine blade, the brief explanation of the design summary will help to understand the design process and configuration of the wind turbine blade structure.
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C. Kong et al. / International Journal of Fatigue 28 (2006) 1382–1388
In this design approach, the optimal blade structural configuration was determined through a parametric study using a finite element method [13]. The skin thickness, the width of the spar flange and the thickness, location and length of the front and rear spar web were optimally redesigned until design criteria were satisfied. The finite element program used for the structural analysis is a well-known commercial code NISA II (numerically integrated element for system analysis) [14]. In this investigation, it is shown that the dominant design parameters are the thicknesses of the spar flange and the skin due to weight reasons, the size of the spar flange and the location of the front and rear spar web for enduring maximum stress or strain, the size of the spar flange for obtaining the proper blade tip clearance, and the location of the front spar web for minimizing the distortion angle. Performing the linear static stress analysis, modal analysis, buckling analysis and additional stress analysis related to ice and thermal loading, it was confirmed that the blade structure is safe and stable operating under the various load cases described above. The joint with the insert bolts at the blade root is a new design concept. It was also proved by the finite element stress analysis that the joint is safe against the design load and fatigue loading conditions. Figs. 2 and 3 show the result of the blade configuration and the cross-sectional views at the middle of the blade, 0.598R station.
Fig. 4. Photograph of the deflected blade under loading by three-point loading fixtures and chain blocks.
In order to evaluate the structural design, a manufactured full scale prototype E-glass/epoxy blade was statically tested (shown as Fig. 4) and the results were compared with the analytical model based on the laminate plate theory and the Tsai–Wu failure criterion. Table 1 shows both measured and predicted results for the mass of the blade, the location of radial center of gravity and the tip deflection measured at the blade tip. Fig. 5 shows the comparison between measured and predicted strain results for the upper part of the blade. Three different locations at the maximum thickness positions of the blade profile, 0.236R(5.56m), 0.493R(11.59m) and 0.547R (13.43m), are presented when the applied load is each 20%, 40%, 60%, 80% and 100% of the maximum design load. The theoretical values are agreed well with experimental measurements. Table 1 Measured and predicted values of the blade
Measured Predicted Error (%)
Mass of blade (kg)
Span-wise center of mass (m)
Tip deflection (mm)
Flap-wise 1st N.F.
2951 2883 2.36
8.451 8.786 3.81
1978.6 1921.0 3.0
1.820 1.856 2.0
Fig. 2. Aerodynamic configuration.
Fig. 3. Cross-section of the blade at 0.598 R station.
Fig. 5. Comparison between measured and predicted strains on the upper part of the blade.
C. Kong et al. / International Journal of Fatigue 28 (2006) 1382–1388
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often used in the fatigue process models are defined as follows:
3. Fatigue load spectrum analysis Because of the complex nature of a load or stress time history, a systematic procedure is required for identifying and counting the individual fatigue cycles in a spectrum. A simple cycle-counting model, which has been successfully used in design of the American wind turbines, such as NASA /DOE Mod-1, Mod-2 and Mod-5B experimental HAWTS and in analysis of field test data from these and other turbines, will be employed for the present study. A time-history of load or stress, which can be obtained in the test during a certain operation, is assumed to be composed of three types of cycles, such as Type I of minimum to maximum during one rotor revolution, Type II of minimum to maximum during one large-scale change in wind speed and Type III of minimum to maximum during one run from startup to shutdown [15]. With this counting model, the number of cycles during a given time period is equal to the run duration divided by the average rotor speed (Type I cycles) plus the number of changes in the wind speed (Type II cycles) plus one Type III cycles. After the individual fatigue cycles in the spectrum were identified and the related parameters were tabulated, a statistical analysis is usually required to convert the resulting time-history data into fatigue design information. At the beginning of the design, there was generally no fatigue load spectrum data. Because this design of the medium scale HAWT was first time in Republic of Korea, a load spectrum that was measured during the conceptual design of a large scale HAWT in America was utilized in order to obtain the usable fatigue load spectrum. Fig. 6 shows a sample fatigue load spectrum in time order. A run period is firstly divided into layers of various durations, when the wind speed and the maximum and minimum loads are relatively constant. Three parameters that are
Lavg ¼ 0:5ðLmax þ Lmin Þ Lcyc ¼ 0:5ðLmax Lmin Þ Lmin Rf ¼ Lmax
ð1Þ ð2Þ ð3Þ
where Lmax, and Lmin is the maximum and minimum loads in one fatigue cycle, Lcyc, cyclic load or load amplitude, Lavg, average or mid-range load, and Rf, fatigue cycle shape parameter or R-ratio. In order to divide into three types of cycle amplitude, the cyclic load ratios are normalized with respect to the mean cyclic load ratio in the spectrum (i.e., divided by 0.212 in this case). Fig. 7 shows a log normalized cyclic load ratios versus normal probability distribution.
Fig. 7. Log cyclic load ratio-normal probability distribution of wind turbine.
Fig. 6. Sample fatigue load spectrum in time order.
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4. Fatigue load estimation Spera proposed the empirical equations, which were based on a set of test data that was broad enough in scope to include the sizes and types of rotors and towers, the types of terrain, and the types of wind conditions expected for future HAWT power stations. Calculation of dynamic loads with these equations is essentially a process of interpolation rather than extrapolation. And in this calculation, structural-dynamic computer models are not required. With the equations presented by Spera, the log-normal probability distributions of the following four important dynamic loads can be calculated from the basic configuration and site data: blade cyclic flapwise moments, blade cyclic chordwise moments, generator cyclic power, and rotor cyclic thrust [16]. However, because we are interested in the blade design only, the flapwise and chordwise cyclic moments will be only calculated in this study. Even though the empirical formulae derived by Spera was obtained from the test data set of two-bladed HAWTS, the empirical formulae can be extended to three-bladed HAWTS [16]. Furthermore, this is enough for a preliminary conceptual design and a base line design purposes. The empirical formulae by Spera are effectively fitted at the 50th and 98th percentile cyclic loads are as follows [10]: dM y;n ¼ a M g sin h þ 432 ð1 þ 1:47aÞ c d 4 D ðg þ 0:012bÞ U n ð1 sÞ expð0:134nÞ 100 ð4Þ dM z;n ¼ e M g þ 46:8 c d ðg þ 0:100bÞ 3 D U n ð1 sÞ exp ð0:276nÞ ð5Þ 100 where dMy = blade cyclic flapwise bending load (kN m), n, number of standard deviation, r, from the mean in a lognormal probability distribution, n = 0 for the 50th percentile load (50% probability of exceedance), n = 1 for the 84th percentile load, n = 2 for the 98th percentile load (2% probability of exceedance), n = 3 for the 99.9th percentile load (0.1% probability of exceedance), a = 0.5(1 cos 2d3): hub-rigidity factor, b = tower blockage factor, b = 2.5 upwind truss, b = 1.0 upwind shell, b = 0.2 downwind shell, c = 50 ct/D: tip-chord factor, d = 1 0.00009(Z + H): air density factor, e = 1/[1 (N/xc)2]: chordwise dynamicamplification factor, f = 1/[1 (N/xf)2]: flapwise dynamic-amplification factor, g = aD/H: wind-variation 10:55 logðU 0 Þ factor, a ¼ a0 10:55a : wind shear power-law expo0 logðH =10Þ 0:2
nent, a0 ¼ ðZ100 Þ : surface-roughness exponent, d3 = inclination of teeter axis from a normal to the blade axis () (rigid hub: d3 = 90), ct = blade chord at tip (m), D = rotor diameter (m), Z = site elevation above sea level (m), H = elevation of rotor hub above ground level (m), N = rotor speed (rpm), xc = blade first chordwise natural frequency (cpm) (If the blade natural frequencies are not known, they can be assumed to be xc = 202-D, xf = 151-D), Z0 = surface roughness length (m), U0 = 50th percentile (med-
ium) free-stain wind speed at hub elevation (m/s), Mg = blade maximum static gravity moment (kN m), [= mass · 9.8 · c.g. or Mg = 0.80 (dMz,0)1.025], h = hub coning angle (), s = blade station at which loads are measured, as a fraction of span, Un = Wind speed at hub elevation that isnr from the mean in a log-normal probability distribution (m/s) U1 = U0 · 1.36, U2 = U0 · 1.86, U3 = U0 · 3.45, dMz = blade cyclic chordwise bending load (kN m). Therefore, in order to calculate cyclic loads by the Spera’s empirical formulae, engineering data for the studied wind turbine rotor blade are applied to empirical formulae as follows: D = 50.5 m, d3 = 90 (Rigid hub), Ct = 0.586 m, Z = 15 m, H = 50 m, N = 27 rpm, xc = 122.04 cpm, U0 = 7 m/s, U1 = 9.5 m/s, U2 = 13.02 m/s, U3 = 24.15 m/s, Mg = 248.2 kN m, h = 0., s = 0.01 R, a0 = 0.02, a = 0.289, a = 1, b = 1.0, c = 0.58, d = 0.994, e = 1.0514, and g = 0.292. In order to obtain My,nmax and Mz,nmax, average R-ratio obtained from the fatigue load spectrum analysis can be used by the following equation: Lcyc 0:5ð1 RÞ ¼ 0:46 ¼ Lavg 0:5ð1 þ RÞ
ð6Þ
Therefore, Lave = Lcyc/0.46, Lmax = Lavg + Lcyc and Lmin = Lave – Lcyc. Table 2 shows calculation results for blade flapwise and chordwise bending moments. 5. Allowable fatigue stress One of the simplest models of the accumulation of fatigue damage during repeated cycles of stress is the linear damage hypothesis, proposed by Palmgren and Miner [11,12]. According to this hypothesis, if the stress cycle remains constant throughout a fatigue lifetime equal to N, then the fraction of that lifetime consumed on every cycle is constant and equal to 1/N. This fracture is also defined as the damage per cycle, and it follows that the total damage at failure is equal to unity. If a stress spectrum is subdivided into group of cycles or layers within which the stress cycles are relatively uniform, then m
I X ni ¼1 N i 1
or
m¼
Nf I P ni
ð7Þ
1
where i, index of layers in the spectrum, I, number of layers in one spectrum, m, number of repetitions of the spectrum required to cause fatigue failure, Ni, fatigue lifetime at a constant stress level Si (cycles), Nf, fatigue lifetime under spectrum loading (cycles), ni, number of cycles applied at stress level Si, Si, stress parameter in the cycle upon which fatigue damage is primarily dependent (MPa). The dependence of N on repeated cycles at a constant level S, illustrated by the S N curve, is typically expressed by a power-law equation as: S ¼ S1N a
or
S P Se
ð8Þ
C. Kong et al. / International Journal of Fatigue 28 (2006) 1382–1388 Table 2 Blade cyclic/max flapwise and chordwise bending moments calculated by Spera’s empirical formulae N
dMy,n (kN m)
dMz,n (kN m)
My,n max
Mz,n max
0 1 2 3
76.63 119.15 186.33 395.17
269.54 276.34 288.67 328.72
243.22 378.18 591.40 1254.24
855.50 877.10 916.20 1043.33
where S1, empirical stress coefficient (MPa), a, empirical exponent, Se, endurance limit, below which no fatigue damage occurs (MPa). If the S–N curve for unidirectional fiberglass material as presented in the reference [17] is used for this study, the empirical exponent a of the empirical equation is assumed to be 1/13.5. And the empirical stress coefficient S1 can be obtained to be 711 Mpa for tensile stresses and 1200 Mpa for compressive stresses from the measured material property data, respectively. The empirical coefficient S1 must be modified by using the Goodman diagram since the S–N curve shown in
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Fig. 7 is at an R-ratio of 0.1, whereas the average R-ratio in Table 2 is 0.37 [10]. The line along which the combinations of the cyclic stress and the average stress produce a constant R-ratio of 0.37 can be drawn in the Goodman diagram. Its slope can be calculated as Scyc/Savg = 0.46 from Eq. (6). From the Goodman diagram the stress cycle parameters at the intersection of this R-ratio line and the fatigue strength line for 108 cycles to failure of the specified UD E-glass/epoxy material are Scyc = 64 MPa, Savg = 139 MPa and Smax = 203 MPa for tensile stress, and Scyc = 107 MPa, Savg = 232.5 MPa and Smax = 339.5 MPa for compressive stress, respectively. The S–N curve for the average fatigue strength of laboratory specimens with an R-ratio of 0.37 becomes For tensile stress, S 0max
N ¼ 203 108
1 13:5
For compressive stress,
Fig. 8. Stress contour under maximum fatigue load.
1
¼ 794:5N 13:5
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C. Kong et al. / International Journal of Fatigue 28 (2006) 1382–1388
1 13:5 N 1 ¼ 1328:7N 13:5 ð9Þ 8 10 Therefore, it can be determined that S 0I ¼ 749:5 MPa for tensile stress, and S 0I ¼ 1328:7 MPa for compressive stress. The allowable fatigue stress Smaxmax for the loading condition represented by Lmaxmax can be calculated by " P 1 # a ni s a S max max ¼ S 0I N f P i ð10Þ ni
S 0max ¼ 339:5
where I X
ni ¼ 19105 cycles;
1
36 X
ni s13:5 ¼ 1864 cycles i
1
h 19105 cyc ¼ 3:72 108 cycles N f ¼ 20 yr 8760 yr 9:0 hr Therefore, the allowable fatigue stresses based on laboratory specimens become 218.8 MPa for tensile stress and 366.0 MPa for compressive stresses. For practical values of allowable stresses, knockdown facts should be considered. In this study, a knockdown factor is assumed to be 0.7, i.e., allowable fatigue stresses are 180.74 MPa for tensile stress and 302 MPa for compressive stress. This value of Smaxmax becomes the allowable fatigue stress for the loading condition represented by Lmaxmax. Therefore, the dynamic structural problem can be converted into a static structural design problem by this method. 6. Evaluation of fatigue life In order to perform comparison between the allowable fatigue stress for 20 year fatigue life and the estimated fatigue stress by the Type II fatigue load (Lmaxmax) from the Spera’s empirical formulae, the calculated maximum flapwise and chordwise bending moments in Table 2 (n = 2) are applied to the finite element model of the wind turbine rotor blade. According to the FEM analysis results, the maximum tensile and compressive stresses are 62.87 MPa and 55.19 MPa, respectively. Fig. 8 shows stress distribution at the spar layer under maximum fatigue load. Therefore, because the safety factors for the allowable fatigue stresses are 3.5 for tensile and 6.6 for compressive, the designed wind turbine blade satisfies the design criteria for the fatigue life of 20 years. 7. Conclusion In this study, the fatigue life for operating more than 20 years was estimated by using the well-known S–N linear damage equation, the load spectrum and Spera’s empirical formulae. From the sample load spectrum data during short period operation, the spectrum data were rearranged as Layer
No., wind speeds, cycles per layer, normalized maximum, minimum, cyclic and average loads, and stress ratios in time order, and then reordered as cyclic loads/median cyclic load, cycles per layer, cumulative cycles, probability of exceeding, and types of cycles, such as Type I, II and III. Fatigue loads, such as flapwise and chordwise bending moments were calculated by Spera’s empirical equations with various engineering data of the studied blade for probability of exceeding. And the allowable fatigue strengths were determined from laboratory fatigue property data for the S–N curve of E-glass/epoxy by Mandell, empirical coefficients by Goodman diagram with the modified stress ratio, and the required design life. In this study, the allowable fatigue strengths were 181 MPa for tension, and 302 MPa for compression, and the applied fatigue stresses were 63 MPa for tension and 55 MPa for compression. Therefore the blade satisfies the design criteria for the fatigue life over 20 years because of sufficient safety factors. References [1] Ackermann T, So¨der L. Wind energy technology and current status. Renew Sust Energ Rev 2000;4:315–74. [2] Wind power monthly industrial magazine. Monthly published since 1985, ISSN 0901-7318. [3] Kim JS. Renewable energy development and supply in Korea. Ministry of Commerce: Industry and Energy and Korean Energy Management Corporation; 2000. [4] Kong C, Bang J, Kim H. A study on aerodynamic analysis and starting simulation for horizontal axis wind turbine blade. J KSPE 1999;3(3):40–6. [5] Kong C, Jeong J. Improvement of design by structural test for 750 kW HAWT composite blade. J KSPE 2000;4(3):22–9. [6] Kong C, Bang J, Jeong S, Ryu J, Kim Y. Structural design of medium scale composite wind turbine blade, APCATS 2000. In: Proceedings of the third asian-pacific conference on aerospace technology and science, 2000;376–384. [7] Kong C, Jeong S, Jang B, Bang J. Design improvement on wind turbine blade of medium scale HAWT by considering. J KSPE 2000;4(3):29–37. [8] Kong C, Kim J. Structural design of medium scale composite wind turbine blade. KSAS Int J 2000;1(1). [9] Kong C, Bang J, Kang M, Jeong S, Yoo J. Structural design of medium scale composite wind turbine blade, ICCM-13. In: 13th international conference on composite materials, 2001. [10] Spera DA. Wind turbine technology fundamental concepts of wind turbine engineering. ASME Press; 1994. [11] Palmgren A. Die Lebendauer von Kugellagern. Zeitschrift von Deutche Ingenieurring 1924;68:339–41. [12] Miner MA. Cumulative damage in fatigue. J Appl Mech 1945;12:A-159–64. [13] Bechly ME, Clausent PD. Technical note: structural design of a composite wind turbine blade using finite element analysis. Comput Struct 1997;63(3):639–46. [14] EMRC NISAII-User’s manual version5.2, 1992. [15] Finger RW. Methodology for fatigue analysis of wind turbines. In: Proceeding Windpower’85 conference, 1985;52–56. [16] Spera DA. Dynamic loads in horizontal-axis wind turbines part II: empirical equations. Windpower’93, 1993;282–289. [17] Mandell JF, Reed RM, Samborsky DD. Fatigue of fiberglass wind turbine blade materials. Albuquerque, New Mexico, SAND92-7005: Sandia National Laboratories; 1992.
International Journal of Fatigue 28 (2006) 1382–1388
www.elsevier.com/locate/ijfatigue
Investigation of fatigue life for a medium scale composite wind turbine blade Changduk Kong
a,*
, Taekhyun Kim a, Dongju Han b, Yoshihiko Sugiyama
c
a Department of Aerospace Engineering, Chosun University, #375 Seosuk-dong, Kwangju, Republic of Korea Sunaerosys Inc., Research Institute, #248-1, Songwon-ri, Nam-myun, Yunki-gun, Chung-Nam, Republic of Korea Department of Mechanical and System Engineering, Ryukoku University, 67 Tsukamoto-cho, Fukakusa Fushimi-ku, Kyoto, Japan b
c
Available online 23 March 2006
Abstract In order to satisfy fatigue requirements in designing a cost effective wind turbine, the wind turbine blade, which is an expensive key component of the wind turbine system, must achieve very long operating life of 20–30 years. In this study, the fatigue life of a medium scale (750 kW) horizontal axis wind turbine system (HAWIS), which has been developed by the present study, was estimated by using the well-known S–N damage equation, the load spectrum and Spera’s empirical formulae in order to confirm more than 20 years operating life. A specific fatigue procedure was proposed with the following three steps. Firstly, from the sample load spectrum data during short period operation, the spectrum data were rearranged as layer numbers, wind speeds, cycles per layer, normalized maximum, minimum, cyclic and average loads, and stress ratios in time order, and then the rearranged data were recorded as cyclic loads per median cyclic load, cycles per layer, cumulative cycles, probability of exceeding, and types of cycles, such as Type I, II and III. Secondly, fatigue loads, such as flapwise and chordwise bending moments were calculated by Spera’s empirical equations with various engineering data of the studying blade for probability of exceeding. Finally, the allowable fatigue strengths were determined from laboratory fatigue property data for the S–N curve of E-glass/epoxy obtained by Mandell, empirical coefficients derived by Goodman diagram with the modified stress ratio and the required design life. In prediction of the fatigue life, it was confirmed that the composite wind turbine blade satisfies the design criteria for the 20 years fatigue life because of sufficient safety margins from the fatigue requirement. 2006 Elsevier Ltd. All rights reserved. Keywords: Composite wind turbine blade; Fatigue life; S–N damage equation; Spera’s empirical equations
1. Introduction The fast progress in wind energy technology and wide spread usage of wind turbines require a standardization of the wind turbine main components aiming at a further cost reduction. This is related not only to large volume production and standardization of production methods but also to material test methods and design rules [1,2]. In South Korea, since the introduction of the ‘‘New and Renewable Source of Energy (NRSE) Development & Promotion Act’’ in 1987, the Korean government has invested *
Corresponding author. Tel./fax: +82 62 230 7188. E-mail address: [email protected] (C. Kong).
0142-1123/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2006.02.034
considerably on the development of a new wind turbine system. One of these initiatives resulted in the design and manufacturing of an E-glass/epoxy composite blade for a 750 kW medium-scale horizontal axis wind turbine system (HAWTS) [3]. The first author and his co-workers have contributed considerably to the structural design and analysis, manufacturing and structural testing of this medium scale composite blade [4–9]. This study developed specific structural design and test procedure for the medium scale E-glass/epoxy composite wind turbine blade through performing aerodynamic design, dynamic and static load analyses, structural design, securing structural strength by static structural analysis, prediction of fatigue life from the random load spectrum,
C. Kong et al. / International Journal of Fatigue 28 (2006) 1382–1388
the modal analysis to prevent the resonance, the structural test with specific test rigs, fixtures and measuring equipments, etc. Furthermore, this study describes a specific blade root joint with inserted bolts and a specific structural configuration, such as the cell box type using the skin-spar-foam sandwich structure not only to minimize the blade weight but also to obtain the structural stability against buckling and vibrating. Among design activities, the cost effective design of the wind turbine structure is one of the most important design works. In order to meet this condition, the wind turbine blade, which is one of the major components of the wind turbine system, must meet the fatigue life requirement of 20–30 years. Fatigue life is usually expressed by term of cycles of failure, which is the number of repetitions of significant loads that can be sustained until initiation and propagation of cracks to an allowable length. Generally the curve of allowable cyclic stress against the number of cycles of failure is called as the S–N curve. Fatigue life is very sensitive to the amplitude of stress variations. In order to account the stress spectrum effect successively, there are two general methods, such as the S–N linear damage and the fracture-mechanics methods [10]. The linear damage hypothesis, which is one of the simplest methods of the accumulation of fatigue damage during reported cycles of stress, was proposed by Palmgren [11] and Miner [12]. According to this hypothesis, if the stress cycle remains constant throughout a fatigue lifetime equal to N, then the fraction of that lifetime consumed on every cycle is constant and equal to 1/N. This fracture is also defined as the damage per cycle, and the total damage at failure is equal to unity. A fracture-mechanics model with the fatigue damage process is more complex than the S–N linear damage model. But many fatigue specialists considers that the most representative model of the physical processes leading to fatigue failure is the fracture-mechanics model. The fracture-mechanics analysis is a validated tool in structural engineering, and the application of this tool for the wind turbine design is straightforward. Fatigue design methodology, experience and verification by field tests are much more critical to success [10]. A fundamental concept of the fracture-mechanics method is that all structures contain small flaws when they are first placed in service. The size of these pre-existed or initial flaws is related to the inspection methods used and the specified acceptance criteria. Flaws in critical areas develop into cracks when fatigue loads are applied, and these cracks continue to grow in length or propagate during in service life of the structure. Crack length is the measure of fatigue damage, and the crack propagation rate is a highly non-linear function of crack length and elapsed time. At the start of service, crack lengths and crack propagation rates are very low. As the crack grows the propagation rate accelerates. Eventually a crack length is
1383
Fig. 1. Fatigue design procedure of medium scale composite wind turbine blade.
reached that is unstable, the propagation rate becomes infinite, and fracture occurs. In this study, a specific fatigue design procedure is proposed as show in Fig. 1. This fatigue design procedure is based on the previous studies, such as the statistical analysis of fatigue loads and stress spectra, calculation of fatigue loads by Spera’s empirical formulae and estimation for the fatigue allowable strength by the S–N linear damage method proposed by Palmgren and Miner [10–12]. 2. Design summary of the composite wind turbine blade Prior to discussion on the fatigue life of the composite wind turbine blade, the brief explanation of the design summary will help to understand the design process and configuration of the wind turbine blade structure.
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In this design approach, the optimal blade structural configuration was determined through a parametric study using a finite element method [13]. The skin thickness, the width of the spar flange and the thickness, location and length of the front and rear spar web were optimally redesigned until design criteria were satisfied. The finite element program used for the structural analysis is a well-known commercial code NISA II (numerically integrated element for system analysis) [14]. In this investigation, it is shown that the dominant design parameters are the thicknesses of the spar flange and the skin due to weight reasons, the size of the spar flange and the location of the front and rear spar web for enduring maximum stress or strain, the size of the spar flange for obtaining the proper blade tip clearance, and the location of the front spar web for minimizing the distortion angle. Performing the linear static stress analysis, modal analysis, buckling analysis and additional stress analysis related to ice and thermal loading, it was confirmed that the blade structure is safe and stable operating under the various load cases described above. The joint with the insert bolts at the blade root is a new design concept. It was also proved by the finite element stress analysis that the joint is safe against the design load and fatigue loading conditions. Figs. 2 and 3 show the result of the blade configuration and the cross-sectional views at the middle of the blade, 0.598R station.
Fig. 4. Photograph of the deflected blade under loading by three-point loading fixtures and chain blocks.
In order to evaluate the structural design, a manufactured full scale prototype E-glass/epoxy blade was statically tested (shown as Fig. 4) and the results were compared with the analytical model based on the laminate plate theory and the Tsai–Wu failure criterion. Table 1 shows both measured and predicted results for the mass of the blade, the location of radial center of gravity and the tip deflection measured at the blade tip. Fig. 5 shows the comparison between measured and predicted strain results for the upper part of the blade. Three different locations at the maximum thickness positions of the blade profile, 0.236R(5.56m), 0.493R(11.59m) and 0.547R (13.43m), are presented when the applied load is each 20%, 40%, 60%, 80% and 100% of the maximum design load. The theoretical values are agreed well with experimental measurements. Table 1 Measured and predicted values of the blade
Measured Predicted Error (%)
Mass of blade (kg)
Span-wise center of mass (m)
Tip deflection (mm)
Flap-wise 1st N.F.
2951 2883 2.36
8.451 8.786 3.81
1978.6 1921.0 3.0
1.820 1.856 2.0
Fig. 2. Aerodynamic configuration.
Fig. 3. Cross-section of the blade at 0.598 R station.
Fig. 5. Comparison between measured and predicted strains on the upper part of the blade.
C. Kong et al. / International Journal of Fatigue 28 (2006) 1382–1388
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often used in the fatigue process models are defined as follows:
3. Fatigue load spectrum analysis Because of the complex nature of a load or stress time history, a systematic procedure is required for identifying and counting the individual fatigue cycles in a spectrum. A simple cycle-counting model, which has been successfully used in design of the American wind turbines, such as NASA /DOE Mod-1, Mod-2 and Mod-5B experimental HAWTS and in analysis of field test data from these and other turbines, will be employed for the present study. A time-history of load or stress, which can be obtained in the test during a certain operation, is assumed to be composed of three types of cycles, such as Type I of minimum to maximum during one rotor revolution, Type II of minimum to maximum during one large-scale change in wind speed and Type III of minimum to maximum during one run from startup to shutdown [15]. With this counting model, the number of cycles during a given time period is equal to the run duration divided by the average rotor speed (Type I cycles) plus the number of changes in the wind speed (Type II cycles) plus one Type III cycles. After the individual fatigue cycles in the spectrum were identified and the related parameters were tabulated, a statistical analysis is usually required to convert the resulting time-history data into fatigue design information. At the beginning of the design, there was generally no fatigue load spectrum data. Because this design of the medium scale HAWT was first time in Republic of Korea, a load spectrum that was measured during the conceptual design of a large scale HAWT in America was utilized in order to obtain the usable fatigue load spectrum. Fig. 6 shows a sample fatigue load spectrum in time order. A run period is firstly divided into layers of various durations, when the wind speed and the maximum and minimum loads are relatively constant. Three parameters that are
Lavg ¼ 0:5ðLmax þ Lmin Þ Lcyc ¼ 0:5ðLmax Lmin Þ Lmin Rf ¼ Lmax
ð1Þ ð2Þ ð3Þ
where Lmax, and Lmin is the maximum and minimum loads in one fatigue cycle, Lcyc, cyclic load or load amplitude, Lavg, average or mid-range load, and Rf, fatigue cycle shape parameter or R-ratio. In order to divide into three types of cycle amplitude, the cyclic load ratios are normalized with respect to the mean cyclic load ratio in the spectrum (i.e., divided by 0.212 in this case). Fig. 7 shows a log normalized cyclic load ratios versus normal probability distribution.
Fig. 7. Log cyclic load ratio-normal probability distribution of wind turbine.
Fig. 6. Sample fatigue load spectrum in time order.
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4. Fatigue load estimation Spera proposed the empirical equations, which were based on a set of test data that was broad enough in scope to include the sizes and types of rotors and towers, the types of terrain, and the types of wind conditions expected for future HAWT power stations. Calculation of dynamic loads with these equations is essentially a process of interpolation rather than extrapolation. And in this calculation, structural-dynamic computer models are not required. With the equations presented by Spera, the log-normal probability distributions of the following four important dynamic loads can be calculated from the basic configuration and site data: blade cyclic flapwise moments, blade cyclic chordwise moments, generator cyclic power, and rotor cyclic thrust [16]. However, because we are interested in the blade design only, the flapwise and chordwise cyclic moments will be only calculated in this study. Even though the empirical formulae derived by Spera was obtained from the test data set of two-bladed HAWTS, the empirical formulae can be extended to three-bladed HAWTS [16]. Furthermore, this is enough for a preliminary conceptual design and a base line design purposes. The empirical formulae by Spera are effectively fitted at the 50th and 98th percentile cyclic loads are as follows [10]: dM y;n ¼ a M g sin h þ 432 ð1 þ 1:47aÞ c d 4 D ðg þ 0:012bÞ U n ð1 sÞ expð0:134nÞ 100 ð4Þ dM z;n ¼ e M g þ 46:8 c d ðg þ 0:100bÞ 3 D U n ð1 sÞ exp ð0:276nÞ ð5Þ 100 where dMy = blade cyclic flapwise bending load (kN m), n, number of standard deviation, r, from the mean in a lognormal probability distribution, n = 0 for the 50th percentile load (50% probability of exceedance), n = 1 for the 84th percentile load, n = 2 for the 98th percentile load (2% probability of exceedance), n = 3 for the 99.9th percentile load (0.1% probability of exceedance), a = 0.5(1 cos 2d3): hub-rigidity factor, b = tower blockage factor, b = 2.5 upwind truss, b = 1.0 upwind shell, b = 0.2 downwind shell, c = 50 ct/D: tip-chord factor, d = 1 0.00009(Z + H): air density factor, e = 1/[1 (N/xc)2]: chordwise dynamicamplification factor, f = 1/[1 (N/xf)2]: flapwise dynamic-amplification factor, g = aD/H: wind-variation 10:55 logðU 0 Þ factor, a ¼ a0 10:55a : wind shear power-law expo0 logðH =10Þ 0:2
nent, a0 ¼ ðZ100 Þ : surface-roughness exponent, d3 = inclination of teeter axis from a normal to the blade axis () (rigid hub: d3 = 90), ct = blade chord at tip (m), D = rotor diameter (m), Z = site elevation above sea level (m), H = elevation of rotor hub above ground level (m), N = rotor speed (rpm), xc = blade first chordwise natural frequency (cpm) (If the blade natural frequencies are not known, they can be assumed to be xc = 202-D, xf = 151-D), Z0 = surface roughness length (m), U0 = 50th percentile (med-
ium) free-stain wind speed at hub elevation (m/s), Mg = blade maximum static gravity moment (kN m), [= mass · 9.8 · c.g. or Mg = 0.80 (dMz,0)1.025], h = hub coning angle (), s = blade station at which loads are measured, as a fraction of span, Un = Wind speed at hub elevation that isnr from the mean in a log-normal probability distribution (m/s) U1 = U0 · 1.36, U2 = U0 · 1.86, U3 = U0 · 3.45, dMz = blade cyclic chordwise bending load (kN m). Therefore, in order to calculate cyclic loads by the Spera’s empirical formulae, engineering data for the studied wind turbine rotor blade are applied to empirical formulae as follows: D = 50.5 m, d3 = 90 (Rigid hub), Ct = 0.586 m, Z = 15 m, H = 50 m, N = 27 rpm, xc = 122.04 cpm, U0 = 7 m/s, U1 = 9.5 m/s, U2 = 13.02 m/s, U3 = 24.15 m/s, Mg = 248.2 kN m, h = 0., s = 0.01 R, a0 = 0.02, a = 0.289, a = 1, b = 1.0, c = 0.58, d = 0.994, e = 1.0514, and g = 0.292. In order to obtain My,nmax and Mz,nmax, average R-ratio obtained from the fatigue load spectrum analysis can be used by the following equation: Lcyc 0:5ð1 RÞ ¼ 0:46 ¼ Lavg 0:5ð1 þ RÞ
ð6Þ
Therefore, Lave = Lcyc/0.46, Lmax = Lavg + Lcyc and Lmin = Lave – Lcyc. Table 2 shows calculation results for blade flapwise and chordwise bending moments. 5. Allowable fatigue stress One of the simplest models of the accumulation of fatigue damage during repeated cycles of stress is the linear damage hypothesis, proposed by Palmgren and Miner [11,12]. According to this hypothesis, if the stress cycle remains constant throughout a fatigue lifetime equal to N, then the fraction of that lifetime consumed on every cycle is constant and equal to 1/N. This fracture is also defined as the damage per cycle, and it follows that the total damage at failure is equal to unity. If a stress spectrum is subdivided into group of cycles or layers within which the stress cycles are relatively uniform, then m
I X ni ¼1 N i 1
or
m¼
Nf I P ni
ð7Þ
1
where i, index of layers in the spectrum, I, number of layers in one spectrum, m, number of repetitions of the spectrum required to cause fatigue failure, Ni, fatigue lifetime at a constant stress level Si (cycles), Nf, fatigue lifetime under spectrum loading (cycles), ni, number of cycles applied at stress level Si, Si, stress parameter in the cycle upon which fatigue damage is primarily dependent (MPa). The dependence of N on repeated cycles at a constant level S, illustrated by the S N curve, is typically expressed by a power-law equation as: S ¼ S1N a
or
S P Se
ð8Þ
C. Kong et al. / International Journal of Fatigue 28 (2006) 1382–1388 Table 2 Blade cyclic/max flapwise and chordwise bending moments calculated by Spera’s empirical formulae N
dMy,n (kN m)
dMz,n (kN m)
My,n max
Mz,n max
0 1 2 3
76.63 119.15 186.33 395.17
269.54 276.34 288.67 328.72
243.22 378.18 591.40 1254.24
855.50 877.10 916.20 1043.33
where S1, empirical stress coefficient (MPa), a, empirical exponent, Se, endurance limit, below which no fatigue damage occurs (MPa). If the S–N curve for unidirectional fiberglass material as presented in the reference [17] is used for this study, the empirical exponent a of the empirical equation is assumed to be 1/13.5. And the empirical stress coefficient S1 can be obtained to be 711 Mpa for tensile stresses and 1200 Mpa for compressive stresses from the measured material property data, respectively. The empirical coefficient S1 must be modified by using the Goodman diagram since the S–N curve shown in
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Fig. 7 is at an R-ratio of 0.1, whereas the average R-ratio in Table 2 is 0.37 [10]. The line along which the combinations of the cyclic stress and the average stress produce a constant R-ratio of 0.37 can be drawn in the Goodman diagram. Its slope can be calculated as Scyc/Savg = 0.46 from Eq. (6). From the Goodman diagram the stress cycle parameters at the intersection of this R-ratio line and the fatigue strength line for 108 cycles to failure of the specified UD E-glass/epoxy material are Scyc = 64 MPa, Savg = 139 MPa and Smax = 203 MPa for tensile stress, and Scyc = 107 MPa, Savg = 232.5 MPa and Smax = 339.5 MPa for compressive stress, respectively. The S–N curve for the average fatigue strength of laboratory specimens with an R-ratio of 0.37 becomes For tensile stress, S 0max
N ¼ 203 108
1 13:5
For compressive stress,
Fig. 8. Stress contour under maximum fatigue load.
1
¼ 794:5N 13:5
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1 13:5 N 1 ¼ 1328:7N 13:5 ð9Þ 8 10 Therefore, it can be determined that S 0I ¼ 749:5 MPa for tensile stress, and S 0I ¼ 1328:7 MPa for compressive stress. The allowable fatigue stress Smaxmax for the loading condition represented by Lmaxmax can be calculated by " P 1 # a ni s a S max max ¼ S 0I N f P i ð10Þ ni
S 0max ¼ 339:5
where I X
ni ¼ 19105 cycles;
1
36 X
ni s13:5 ¼ 1864 cycles i
1
h 19105 cyc ¼ 3:72 108 cycles N f ¼ 20 yr 8760 yr 9:0 hr Therefore, the allowable fatigue stresses based on laboratory specimens become 218.8 MPa for tensile stress and 366.0 MPa for compressive stresses. For practical values of allowable stresses, knockdown facts should be considered. In this study, a knockdown factor is assumed to be 0.7, i.e., allowable fatigue stresses are 180.74 MPa for tensile stress and 302 MPa for compressive stress. This value of Smaxmax becomes the allowable fatigue stress for the loading condition represented by Lmaxmax. Therefore, the dynamic structural problem can be converted into a static structural design problem by this method. 6. Evaluation of fatigue life In order to perform comparison between the allowable fatigue stress for 20 year fatigue life and the estimated fatigue stress by the Type II fatigue load (Lmaxmax) from the Spera’s empirical formulae, the calculated maximum flapwise and chordwise bending moments in Table 2 (n = 2) are applied to the finite element model of the wind turbine rotor blade. According to the FEM analysis results, the maximum tensile and compressive stresses are 62.87 MPa and 55.19 MPa, respectively. Fig. 8 shows stress distribution at the spar layer under maximum fatigue load. Therefore, because the safety factors for the allowable fatigue stresses are 3.5 for tensile and 6.6 for compressive, the designed wind turbine blade satisfies the design criteria for the fatigue life of 20 years. 7. Conclusion In this study, the fatigue life for operating more than 20 years was estimated by using the well-known S–N linear damage equation, the load spectrum and Spera’s empirical formulae. From the sample load spectrum data during short period operation, the spectrum data were rearranged as Layer
No., wind speeds, cycles per layer, normalized maximum, minimum, cyclic and average loads, and stress ratios in time order, and then reordered as cyclic loads/median cyclic load, cycles per layer, cumulative cycles, probability of exceeding, and types of cycles, such as Type I, II and III. Fatigue loads, such as flapwise and chordwise bending moments were calculated by Spera’s empirical equations with various engineering data of the studied blade for probability of exceeding. And the allowable fatigue strengths were determined from laboratory fatigue property data for the S–N curve of E-glass/epoxy by Mandell, empirical coefficients by Goodman diagram with the modified stress ratio, and the required design life. In this study, the allowable fatigue strengths were 181 MPa for tension, and 302 MPa for compression, and the applied fatigue stresses were 63 MPa for tension and 55 MPa for compression. Therefore the blade satisfies the design criteria for the fatigue life over 20 years because of sufficient safety factors. References [1] Ackermann T, So¨der L. Wind energy technology and current status. Renew Sust Energ Rev 2000;4:315–74. [2] Wind power monthly industrial magazine. Monthly published since 1985, ISSN 0901-7318. [3] Kim JS. Renewable energy development and supply in Korea. Ministry of Commerce: Industry and Energy and Korean Energy Management Corporation; 2000. [4] Kong C, Bang J, Kim H. A study on aerodynamic analysis and starting simulation for horizontal axis wind turbine blade. J KSPE 1999;3(3):40–6. [5] Kong C, Jeong J. Improvement of design by structural test for 750 kW HAWT composite blade. J KSPE 2000;4(3):22–9. [6] Kong C, Bang J, Jeong S, Ryu J, Kim Y. Structural design of medium scale composite wind turbine blade, APCATS 2000. In: Proceedings of the third asian-pacific conference on aerospace technology and science, 2000;376–384. [7] Kong C, Jeong S, Jang B, Bang J. Design improvement on wind turbine blade of medium scale HAWT by considering. J KSPE 2000;4(3):29–37. [8] Kong C, Kim J. Structural design of medium scale composite wind turbine blade. KSAS Int J 2000;1(1). [9] Kong C, Bang J, Kang M, Jeong S, Yoo J. Structural design of medium scale composite wind turbine blade, ICCM-13. In: 13th international conference on composite materials, 2001. [10] Spera DA. Wind turbine technology fundamental concepts of wind turbine engineering. ASME Press; 1994. [11] Palmgren A. Die Lebendauer von Kugellagern. Zeitschrift von Deutche Ingenieurring 1924;68:339–41. [12] Miner MA. Cumulative damage in fatigue. J Appl Mech 1945;12:A-159–64. [13] Bechly ME, Clausent PD. Technical note: structural design of a composite wind turbine blade using finite element analysis. Comput Struct 1997;63(3):639–46. [14] EMRC NISAII-User’s manual version5.2, 1992. [15] Finger RW. Methodology for fatigue analysis of wind turbines. In: Proceeding Windpower’85 conference, 1985;52–56. [16] Spera DA. Dynamic loads in horizontal-axis wind turbines part II: empirical equations. Windpower’93, 1993;282–289. [17] Mandell JF, Reed RM, Samborsky DD. Fatigue of fiberglass wind turbine blade materials. Albuquerque, New Mexico, SAND92-7005: Sandia National Laboratories; 1992.