FatigueStudy

FatigueStudy

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  The Usage ofParameterized Fatigue Spectra and Physics-Based Systems Engineering Models for Determination of Wind Turbine Component Sizing Taylor J. Parsons∗ , Paul Veers† and Yi Guo‡ National Renewable Energy Laboratory, Golden, CO, 80401. Software models which use design-level input variables and physics-based engineering analysis to approximate the mass and geometrical properties of components in large-scale machinery can be very useful for the analysis of design trade-offs in complex systems. This study uses DriveSE, an OpenMDAO-based drivetrain model which considers stress and deflection criteria to determine the sizing of drivetrain components within a geared, upwind wind turbine. The capability for fatigue analysis is under development and can be implemented in the main shaft and bearing routines. Because a full lifetime fatigue load spectrum is difficult to define without computationally expensive simulations in programs such as FAST, parameterized fatigue loads spectra which depend on wind conditions, rotor diameter, and turbine design life has been implemented as placeholders for future fatigue analysis. This paper details a three-part investigation of the parameterized approach and a comparison of the DriveSE model with and without fatigue analysis on the main shaft system. It compares loads from three turbines of varying size, and determines if and when fatigue governs sizing according to the current model. It then investigates the model’s sensitivity to shaft material parameters. Finally, it showcases the design and analysis capabilities of DriveSE by cycling through the properties of known high-strength steel materials and selecting the one which produces lowest assembly mass. The parameterized fatigue spectra currently used in DriveSE are found to be useful for the sake of comparing the effects of design variables on a system, but require further work in order to improve accuracy and sensitivity to technological improvements on the rotor and controller of a turbine. Nomenclature F Force, N M Moment, N*m γ Shaft angle from horizontal, m Lrb Distance from rotor to upwind main bearing, m Lmb Length between main bearings, m f Frequency, Hz TL Turbine design life, yr. Vmin Cut-in wind speed, m/s Vmax Cut-out wind speed, m/s V0 Nominal wind speed, m/s kw Weibull shape parameter, windspeed probability distribution Aw Weibull scale parameter, windspeed probability distribution, m/s R Rotor radius, m ρa Density of air kg/m3 c Characteristic chord length of blade at r = 2/3R, m ∗Research Participant, National Wind Technology Center, 15013 Denver West Parkway, Golden, CO, AIAA Student Member. †Chief Engineer, National Wind Technology Center, 15013 Denver West Parkway, Golden, CO, AIAA member. ‡Research Engineer, National Wind Technology Center, 15013 Denver West Parkway, Golden, CO. 1 of 19 American Institute of Aeronautics and Astronautics
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  CL Lift coefficientof blade at r = 2/3R, m W Resulting wind speed, m/s X Tip speed ratio B Blade number Subscript c Characteristic load r Rotor mb1 Upwind main bearing mb2 Downwind main bearing Superscript x Coordinate axis x-direction y Coordinate axis y-direction z Coordinate axis z-direction st Stochastic load dt Deterministic load I. Introduction Wind turbine design using software models involves numerous input variables whose effects impact the mass and cost of components throughout the system. Such variables include wind conditions which effect loading, design parameters such as the location and configuration of load-bearing components, and material choices for individual subcomponents of a machine. As a part of the Systems Engineering effort at the National Wind Technology Center, several analysis models have been created whose primary function is to mimic the design process in place for large-scale wind turbines in order to investigate the effects of design changes across an entire turbine or wind plant and optimize configurations for minimum cost of energy. This study uses DriveSE, an OpenMDAO-based drivetrain model which considers stress and deflection criteria to size the main shaft, bearings, gearbox, high-speed shaft, generator, bedplate, and other nacelle components of turbines under numerous configurations. The capability for fatigue analysis is under develop- ment and can be implemented in DriveSE for the main shaft and bearings. This paper details a three-part investigation of the approach and a comparison of the DriveSE model with and without fatigue analysis. It begins by comparing loads from three different turbines of varying size, and determining if and when fatigue governs sizing according to the current model. It then looks at the model’s sensitivity to the fatigue slope exponent of the main shaft material, a variable which has been found to significantly impact component sizing under fatigue. Finally, this paper will showcase the analysis capabilities of DriveSE by cycling through the properties of known high-strength steel materials and selecting the one which produces lowest assembly mass. II. DriveSE Approach A full paper documenting the DriveSE model approach is in the publication process and can be found shortly on the WISDEM (Wind-Plant Integrated System Design and Engineering Model) website.1 A short description of the model and its functions is included here for the purpose of identifying how the effects of fatigue are modeled in DriveSE. As a result of these analyses and further development of the DriveSE fatigue model, future public versions will include both fatigue and extreme-loads driven design. 1. Extreme Loads Analysis DriveSE models the main shaft as a hollow high-strength steel shaft which is normally tapered between upwind and downwind bearings for a four-point suspension drivetrain.1,2 Shaft length depends on a deflection criterion at the location of the main bearings, and shaft diameter depends on the highest stresses experienced at stress concentration locations, typically at the main bearing locations. Figure 1 shows the force diagram of a main shaft in such a drivetrain. The input loads for the shaft and bearing model can be taken from a variety of sources, including 2 of 19 American Institute of Aeronautics and Astronautics
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  simulations such asFAST3 in conjunction with MExtremes.4 A flowchart illustrating the internal shaft and bearing sizing loops is shown in Appendix A, figure V. Bearings are then sized based on the diameter of the shaft at each bearing location. The type of bearing is a user-input design parameter, and can include compact aligning roller bearings (CARB), spherical roller bearings (SRB), single-row tapered roller bearings (TRB1), double-row tapered roller bearings (TRB2), cylindrical roller bearings (CRB), and single-row deep-groove radial ball bearings (RB).1 With fatigue anal- ysis, bearings are selected based on an accrued bearing damage figure which determines whether the bearings are under high-load or low-load applications. Without the additional fatigue analysis, bearing mass and di- mensional data are simply defined from the bore diameter, which is the same as the main shaft diameter at each bearing location. 2. Parameterized Fatigue Analysis A full lifetime fatigue load spectrum is difficult to define without computationally expensive simulations in programs such as FAST.3 Because optimization routines require numerous simulations, an analysis which re-runs these expensive simulations multiple times is not only computationally expensive, but also difficult to accurately connect the effects of input changes on stochastic extreme load outputs. For these reasons, simplified parameterized fatigue loads spectra, which depend on wind conditions, rotor diameter, and turbine design life, have been implemented as placeholders for further fatigue analysis. The benefits for this approach lie in its computational speed and ease of use, but its simplified nature makes it impossible to capture changes in blade design, improvements in controllers, and certain site-specific conditions which are not seen in the model inputs. While recognizing that the loads generated by the parameterized approach are not currently updated or accurate, this study illustrates the application of the fatigue spectra which are based off of the 1992 Danish design standard DS4725 and scaled slightly to match modern technology.1 This section will briefly touch on the calculations involved in the derivation. See Appendix A for the full mathematical description. When calculating the maximum number of load cycles experienced by the drivetrain during the life of the turbine, it is assumed that the rated speed of the turbine, its design life, and probability of operation (taken from wind speed probability Weibull parameters and cut-in/cut-out wind speed) can be multiplied to give an approximate lifetime number of shaft rotations, as in equation 1.1,5 Nf = fcTL(exp(−(Vmin/Aw)kw ) − exp(−Vmax/Aw)kw ) (1) High-cycle fatigue spectra from stochastic wind loading have been found to follow a decreasing logarith- mic relationship in the high-cycle region, from large magnitude loads at lower-cycle counts down to lower magnitude loads experienced up to Nf .5 The parameterized fatigue spectra uses this general shape and scales the magnitude of the loads distributions depending on environmental and rotor design variables. Figure 2 shows the general shape of the force and moment ranges as an exceedance plot for a 750 kW machine with a 48 m rotor diameter. All documentation for this derivation can be found in Appendix C. Note that this plot is of the stochastic load ranges, and does not take into account the impact of mean loads such as rotor weight. The load ranges described above are accompanied by mean values resulting from component weights, operational torque, and mean axial force. As the design flowchart located in Appendix B shows, the model uses the shaft length and diameter(s) from the extreme loads analysis and increases the shaft diameters if the total damage from high-cycle fatigue results in failure before the design life of the turbine. Damage resulting from each load cycle is assumed to be cumulative, and wake effects from neighboring turbines are not considered in the calculation of aerodynamic rotor load cycles. After the fatigue-driven design of the shaft is complete, the model uses the forces experienced at the bearing locations to calculate fatigue-driven design in the bearing routine. For further detail on the methods used in the DriveSE sizing models, refer to the extensive documentation found in the accompanying drivetrain model report.1 III. Methods A. Turbine Comparison In order to illustrate the use of parametric fatigue load models in system design calculations, we compare three reference turbines of varying size, define their accompanying extreme loads inputs, and determine the 3 of 19 American Institute of Aeronautics and Astronautics
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  point at whichfatigue governs the shaft and bearing sizing of each. Load data are taken from FAST (Fatigue, Aerodynamics, Structures, and Turbulence) simulations,3 and post-processed in MExtremes.4 All Extreme events are cycled as inputs to the DriveSE model, and the set of loads which produce the most massive components are taken to be the baseline loads inputs for the remainder of the study. The baseline loads for each turbine are included in Table 1. Table 1: Wind turbine base loads Loads 750 kW 1.5 MW 5 MW Fx (kN) 88.305 91.732 254.475 Fy (kN) 2.4435 -77.703 -179.145 Fz (kN) -183.3 -332.64 -1364.85 Mx (kNm) 434.7 949.59 4942.35 My (kNm) -807.222 1336.223 14053.5 Mz (kNm) -375.3 -918.405 -5404.05 Because the fatigue model resizes the main shaft diameters up from those of the extreme loads model, a way of quantifying which load set governs the shaft diameter is needed. A multiplier is added to the set of baseline loads and scaled linearly until the point at which the shaft diameters transition from fatigue governance to extreme loads governance. If the extreme loads multiplier at the transition point is greater than 1, then fatigue governs sizing under normal conditions, according to the model. In this way, the multiplier at the transition point is used as a gage of which loads set governs shaft sizing and by how much. 1. GRC 750 kW Turbine The GRC (Gearbox Reliability Collaborative) 750 kW Turbine is a stall-regulated, three-bladed upwind turbine which resulted from an NREL effort to reveal the causes and loading conditions that result in gearbox failures.14 Its simple modular configuration and open-source design have been used in several alternative designs as a baseline design and for illustration of a typical drivetrain configuration. Despite the GRC turbine’s three-point suspension design, this study defines the machine as four-point suspension for the purpose of analyzing and comparing the fatigue effects on downwind bearings for all three turbine sizes. Further turbine characteristics are included in Table 2.a 2. WindPACT 1.5 MW Turbine The WindPACT (Wind Partnership for Advanced Component Technologies) 1.5 MW Turbine is the result of an NREL-funded study on how new technologies and larger rotors would affect the cost of energy.12 The WindPACT study examined several nameplate sizes, however we focus only on the 1.5 MW nameplate baseline design as it is similar to the GE 1.5 MW turbine that is commonly installed in the U.S. Similar to the NREL 5.0 MW Reference Turbine, the WindPACT 1.5 MW turbine is a three bladed, upwind, variable speed, variable pitch wind turbine design. Details on the WindPACT 1.5 MW are also included in Table 2. 3. NREL 5 MW Turbine The NREL 5 MW Reference Turbine is a conventional utility scale turbine with a three-bladed upwind, variable speed, variable pitch design. It is loosely based on the REpower 5M, RECOFF (Recommendations for Design of Offshore Wind Turbines),6 and DOWEC (Dutch Offshore Wind Energy Converter)7 designs and is a representative design for offshore turbines of a similar nameplate power rating. It is commonly used as a baseline design for wind energy research on diverse topics such as hydrodynamics of floating turbines,8 blade design,9 and many others. Relevant geometrical and mass properties for the NREL 5 MW Reference aGRC was mainly concerned with the input torque to the gearbox, and accordingly ran only the DLCs which may produce a failure event in this assembly: DLC’s 1.2-1.5, 6.1, 6.3, and 7.1 were analyzed and re-run through MExtremes for the purpose of this study. 4 of 19 American Institute of Aeronautics and Astronautics
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  Table 2: Windturbine specifications 750 kW 1.5 MW 5 MW Rotor Diameter (m) 48.2 70 126 Hub Height (m) 55 84 90 Cut-in, Rated, Cut-out Wind Speed(m/s) 3,16,25 4,16.18,25 3,11.4,25 Gearbox Ratio 81:1 78:1 97:1 Overhang Distance (m) 2.26 3.3 5 Lrb (m) † 1.22 1.535 1.912 Tower Top Diameter (m) 2.2 2.3 3.78 † See Figure 1 for graphical definition. Important moment arm from rotor loads to upwind bearing. Turbine and its drivetrain are given in Table 2, which are found from Jonkman, 2009.10 Loads data were located from a 2014 NREL study on the effects of tip speed constraints on optimized design.11b bThis study did not run all Design Load Cases for the turbine, notably omitting DLC 1.4, 6.2, and 6.3 due to lack of yaw controller in simulations. In other turbines where these DLCs were run, they did not contain the baseline loads selected. 5 of 19 American Institute of Aeronautics and Astronautics
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  Blade Upwind Bearing Main Shaft Wms Wgb Fmb1 Fgb Las Lbg Wa1 Lms Lgc z z z x y Mmb1 y x Fmb1 y Mmb1 z x Fgb y Lgb COG HighSpeed Shaft Gearbox x Generator Coupling Fgc Fgc y z Mgc y Mgc z Mgb y Mgb z Fmb1 x Fgb x Fgc x Gearbox Trunnion Wr Mr y Mr z Fr x Lrb x Hgb Hgc x Downwind Bearingx Lmb Fmb2 z Mmb2 y Fmb2 y Mmb2 z Fmb2 x g Shrink Disk Wa2 Brake Disk Figure 1: Force diagram of a main shaft in a four-point suspension drivetrain, courtesy of Yi Guo1 6 of 19 American Institute of Aeronautics and Astronautics
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  Figure 2: Stochasticwind force and moment cyclic amplitude spectra defined by DS472 using inputs from a generic 750 kW rotor. 7 of 19 American Institute of Aeronautics and Astronautics
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  B. Fatigue ExponentSensitivity An investigation of the model’s sensitivity to the main shaft fatigue exponent is performed in order to show the significant impact this variable can have on the design of components in high-cycle fatigue situations, and determine if the default value is suitable for general analysis in which the material properties of components are not known.c Keeping all other inputs equal, we cycle through the exponent range from 0.6 to 0.12, which encapsulates high-strength steels which are commonly used in main shafts.1,18,19 The data is processed to find at which loads multipliers fatigue no longer resizes the main shaft, and conclusions can be drawn from the relationship between fatigue exponent and transition point. This yields insight into which set of loads are design drivers at each data point, and with how much confidence. C. Material Analysis This portion of the study shows DriveSE’s capabilities for machine design analysis of individual compo- nents and assemblies. Recognizing that fatigue exponent is closely coupled with a material’s other strength characteristics, the model calculates component and assembly masses after 38 steel materials are applied to the main shaft model. Variables which define the S-N relationship of the metal reflect real-world materials data taken from two sources.18,19 A full input table for this analysis is included in Appendix C. A file with these material properties is run in DriveSE and dimensional results for all affected components are recorded for analysis. For this analysis, all steel densities are assumed to be constant, and the simulation objective is to minimize mass independent of material costsd . IV. Results A. Turbine Comparison Results Figure 3 show the results of manipulating the extreme loads multiplier on the shaft/bearing diameters and bearing masses for the 750 kW machine. Each of the turbines exhibit a pattern where upwind diameters are slightly larger in both extreme loads and fatigue analysis. The transition from fatigue to extreme loads is shown to occur at a higher loads multiplier for the upwind bearing, meaning this model predicts fatigue will govern shaft sizing on the upwind bearing more often than the downwind. The larger difference between bearing masses is reflective of the fact that this study uses heavier CARB bearings which can support the higher loads for the upwind bearings and lighter SRB bearings for the downwind. Table 3 shows the loads multiplier at the transition point for each of the three machines. Fatigue analysis resized the upwind diameters of the two larger turbines, and nearly had an impact on the upwind diameter of the GRC turbine and the downwind diameter of the 5 MW turbine. These results indicate that the parameterized fatigue spectra for fatigue analysis may approximate loads which are uncharacteristically high for turbines with larger rotor diameters. Table 3: Comparison of extreme loads multipliers at transition point by turbine GRC 750 kW WindPACT 1.5 MW NREL 5 MW Upwind Multiplier 0.93 1.31 1.46 Downwind Multiplier 0.76 0.7 0.97 Table 4 compares the shaft dimensions from data sheets to those according to the DriveSE models. We see that in the case of the WindPACT turbine, the fatigue model resizes the shaft to be closer to the expected diameter, but for the 5 MW case, the diameter is too large. This could be due to a variety of reasons, including different material properties for each shaft, the theory that the load ranges are do not scale well for the larger machines, or because the dimensions of the 5 MW shaft are only approximations. Because the dimensions of the GRC shaft are larger than expected regardless of fatigue analysis, one might observe that either the extreme loads from the GRC machine are larger than what the turbine would experience, or the dimensions of the shaft in the GRC machine are not what they would be for a fully cOther sensitivity tests were performed on wind variables such as IEC class and windspeeds, but the parameters manipulated the stochastic load ranges as expected and did not produce any striking conclusions. dMaterial cost data is dependent on several factors, and was not located for the steels used in this study. 8 of 19 American Institute of Aeronautics and Astronautics
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  Figure 3: GRC750 kW Bearing Diameter and Mass results with Fatigue-Extreme Load Transition Table 4: Comparison of shaft diameters with and without fatigue Property GRC 750 kW WindPACT 1.5 MW NREL 5 MW Actual Dimensions Upwind Diameter (m) 0.38 0.60 1.00* Downwind Diameter (m) 0.33 0.51 0.72* Design Without Fatigue Upwind Diameter (m) 0.40 0.48 0.96 Downwind Diameter (m) 0.36 0.48 0.87 Design With Fatigue Upwind Diameter (m) 0.40 0.53 1.09 Downwind Diameter (m) 0.36 0.48 0.87 * In the 5 MW case, approximate diameters were calculated from torsional stiffness and length constraints10 due to a lack of specified dimensions.1 designed and manufactured machine of its size. On the first point, the GRC turbine is simulated as a stall-regulated machine,14 which would change the aerodynamic rotor loads from than its pitch-regulated counterparts. This could be why the extreme loads analysis governs shaft sizes for this machine. This would not, however, invalidate the observation that fatigue dominates sizing for larger turbines, because according to Table 3 the effects of fatigue are significantly more pronounced for the 5 MW turbine than for the 1.5 MW turbine, which are both pitch-regulated machines. On the second point, it is important to note that the GRC 750 was created for the purpose of studying gearboxes, and that the optimal size for other components were not thoroughly studied. The results of this analysis show that the approach which couples FAST loads outputs to DriveSE is relatively accurate with both extreme loads analysis and the additional fatigue option. However, the model does not accurately capture the effects of every input parameter on the shaft assembly dimensions. One important conclusion from this comparison is that the parameterized fatigue spectra, which were originally derived for small-scale stall-regulated machines, may not reflect the fatigue loads coming from the rotors of larger, more modern turbines as accurately as software models require. This shortcoming is especially pronounced if changes to rotor or controller design are made which do not impact the limited fatigue input 9 of 19 American Institute of Aeronautics and Astronautics
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  parameters. B. Fatigue ExponentSensitivity Results Figure 4 shows the effects of manipulating shaft fatigue exponents on the main shaft model for the 5MW turbine, assuming constant ultimate strengths. From a fatigue exponent of -0.12 to -.10, the model exhibits a transition from fatigue determining the size of both bearings to having no effect on sizing. This exemplifies the fact that shaft design under fatigue is highly sensitive to this parameter. Figure 4: Effects of shaft strength exponent on which loads determine shaft sizing These results span the range of exponents observed in high-strength steel alloys commonly found in wind turbine main shafts. However, if lower-strength alloys were used in this model, the results would either be massive shafts and bearings which increase the mass and cost of the nacelle, or components which will experience high-cycle fatigue failure within their operational lifetimes. Regardless of the accuracy of the fatigue loads spectra used in the model, future efforts to model components under fatigue loading must pay close attention to the material properties selected for their components. As Figure 4 conveys, the model’s default exponent of -0.117, the one which was used in the turbine comparison, will often emphasize fatigue effects more than other high-strength steel properties. If mass savings were the only objective, a lower-exponent material should always be selected. C. Materials Analysis Results The results of the 5MW shaft design with all properties from the material table applied to the model are plotted in figures 6 and 5. A full table with assembly masses, diameters, and nacelle masses from each material simulations is located in Appendix C. From Figure 5 we see that the strength of the shaft affects the sizing as we might expect. The ultimate tensile strength helps to define both the yield stress criteria on which the main shaft is sized under extreme loads, and the point at which the material fails at N=1 cycles on the S-N curve. Because of this strong coupling to both analysis techniques, very little scatter exists in Figure 5. The relationship between fatigue exponent and assembly mass shown in 6 is still a defined downward trend, but with significantly more ”noise” because this variable does not always have an effect on shaft sizing. Even when fatigue does not have an effect on the diameter of the shaft, this relationship would still be present because fatigue exponents of a lower magnitude are normally accompanied with higher strengths. 10 of 19 American Institute of Aeronautics and Astronautics
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  Figure 5: Ultimatetensile strength vs main shaft and bearing assembly mass Figure 6: Fatigue exponent vs main shaft and bearing assembly mass If a design were to be completed with these material possibilities and with the explicit goal of minimizing mass, SAE 1045 quenched and tempered steel, with Sut = 1584 MPa and b = −.06 should be used because of its combination of high ultimate strength and lowest magnitude fatigue exponent. From a comparison of nacelle masses between material choices we can see the compounding effects of the shaft and bearing assembly mass on the overall nacelle. While the main shaft and bearings typically only comprise 8.6% of the nacelle mass according to these results, they impact the sizing of the bedplate so that a 20% increase in bearing and shaft mass translates to a 4.8% change in total nacelle mass. Contrast this with the 1.71% change in nacelle mass if such an increase had no impact on other components. This demonstrates the importance of accuracy on the component level within the model, and shows that improvements in optimized design of turbine components could have a significant impact on the capital cost of a turbine. V. Conclusion Due to its purely physics-based sizing approach, a comparison between DriveSE outputs and known dimensions demonstrates that the model is relatively accurate for each of the three turbines. It is illustrated that the sizing of the main shaft, and consequently the size of the bearings and bedplate, are very sensitive to the main shaft fatigue exponent. If using the DriveSE fatigue analysis in the future, great care must 11 of 19 American Institute of Aeronautics and Astronautics
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  be taken toensure accurate material properties are used. For the purposes of general case studies and modeling, the default fatigue exponent of -0.117 and tensile strength of 700MPa is shown to be a reasonable representation of main shaft materials used in the commercial-scale wind industry. These default parameters have been demonstrated to resize the upwind bearing of a four-point suspension drivetrain more frequently than the downwind bearing due to the higher magnitudes of cyclic loads experienced at this location. The parameterized fatigue loads approach is shown to be a workable means of including the fatigue assessment in a system optimization study. However, much work is yet to be done to accurately define the parameterized load spectra for a particular turbine design for the large, pitch-controlled, current generation of advanced wind turbines. 12 of 19 American Institute of Aeronautics and Astronautics
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  Appendix A: FatigueLoads Definition The aerodynamic stochastic loads spectra originate from a Danish Standard published in 1992.5 This standard gives an idealized load distribution expressed in terms of wind speed characteristics, IEC class,15 the design life of the turbine (generally 20 years), rotor diameter and rated rpm. DS472 is based on the aerodynamic line load on the blades, p0 [N/m], and is calculated in Eq. 2. The load distribution along a single blade is then represented as a triangular line load with a value of p0 at the blade tip and 0 at the hub. This value comes into play in subsquent calculations of aerodynamic loading on the rotor: po = 1 2 ρaW2 cCL (2) where the resulting windspeed, W, is found from the following: W2 = 4π 3 frR 2 + V 2 0 (3) To limit the number of inputs needed for the fatigue model, a generalized chord length was calculated from the optimization equation found in,17 shown in Eq. 4. In studies involving an entire turbine, this variable is linked to the WISDEM rotor model, RotorSE. c(r) = 16πR 9BCL 1 X X2 r R 2 + 4 9 (4) Combining Eqs. 2, 3, and 4 result in a simplified equation for the aerodynamic line load on the blades: po = 4 3 ρa 4π 3 2 + V 2 0 ∗ π ∗ R BX √ X2 + 1 (5) To define the total number of load cycles experienced throughout the turbine life, the probability of operation is approximated from the cut-in and cut-out wind speeds and the U10 Weibull parameters. This probability is then multiplied by the number of rotor rotations during the design life, if the turbine were operating at rated speed the entire time. Equation 1 in the body of the text defines NF , the maximum number of loads experienced from a load frequency, fc. To evaluate pressure from the blades of a turbine, fc is taken to be frated ∗ B, as recommended by the standard. This effectively defines the total number of possible load cycles as 3 × Nrotor for a three-bladed turbine and 2 × Nrotor for a two-bladed turbine. To define a stochastic cyclic load, a standardized, nondimensional load range F∆∗ is defined as a repre- sentation of all load ranges up to this maximum number of cycles. Under DS472, the probability distribution is defined such that F∆∗ is the load range that is exceeded N times and is found using the following equation: F∆∗ (N) = β(log10(Nf ) − log10(N)) + 0.18 (6) This creates a definition of the standard load range distribution that shows a low occurrence of high- magnitude loads and a high occurrence of lower magnitude loads. This nondimensional load distribution is used to form the shape of the rotor force and moment distribution for fatigue analysis. Figure 2 shows an example of this distribution shape applied to the rotor force and moment distributions on a 750-kW rotor. The variable β is a scaling variable that takes into account the turbulence intensity, IT , and the 10- min wind speed shape parameter, Aw. β is calculated in Eq. 7. Assuming no adjustment for neighboring turbines, the value for turbulence intensity is found from the user-input IEC class according to Table 5.15 β = 0.11kβ(IT + 0.1)(Aw + 4.4) (7) 13 of 19 American Institute of Aeronautics and Astronautics
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  Table 5: RelationshipBetween IEC Class and Turbulence Intensity Factor IEC Class IT A 0.16 B 0.14 C 0.12 In accordance with DS472, the value of kβ is taken to be 2.5. In addition to scaling the variable β, kβ also appears as an added condition to the standardized loads range found in Eq. 6. The condition suggested by DS 472 is that the value of F∗ ∆ must not exceed 2kβ. This effectively truncates the extreme values of the non-dimensional loads range at approximately 103 to 104 load counts, which is the beginning of the high-cycle fatigue region. With F∗ ∆ and po defined, the stochastic load ranges from the rotor can be calculated according to the relationships in Eq. 8:      Fst x = 0.5F∗ ∆(N)p0RCFx Mst x = 0.45F∗ ∆(N)p0R2 CMx Mst y = 0.33F∗ ∆(N)krp0R2 CMy Mst z = 0.33F∗ ∆(N)krp0R2 CMz (8) The amplification factor, kr, depends on the ratio of rotor resonant frequency (nr) to the lowest resonant frequency of the associated oscillation form (no); for My and Mz, no = nr, leading to an amplification factor value of 0.8. The factors CF x, CMx, CMy, and CMz are adjustments to the original spectra defined by DS 472 to account for technology changes since its publication. These factors were determined using available industry data on lifetime fatigue loads, which are unfortunately proprietary in nature.      CF x = 0.365 × log(Dr) − 1.074 CMx = 0.0799 × log(Dr) − 0.2577 CMy = 0.172 × log(Dr) − 0.5943 CMz = 0.1659 × log(Dr) − 0.5795 (9) An example of the output load ranges is shown in Figure 2 in the body of the text. Note that each of these points represents the range of a cyclic load occurring a specified number of times. Because calculations of stress for the purposes of damage equivalent loads require stress amplitudes to be used, the model halves these values in subsequent calculations. This distribution is treated as a histogram of loads experienced across the turbine life. A plot of these distributions, much like those found in Figure 2, is also known as an exceedance plot. In addition to stochastic alternating loads, several deterministic rotor loads are considered for the purpose of fatigue analysis. For example, rotor weight is applied as a deterministic force in the negative z-direction: Fdt z = −Wr (10) From the definition of the line load p0, the mean rotor force in the x-direction is found to be: Fdt x = 1 2 p0RB (11) The mean rotor torque during operation is defined as: Mdt x = P ωηd (12) where P is the power rating of the turbine, ω is the rotational velocity of the rotor and drivetrain, and ηd is the drivetrain efficiency.5 These mean loads are applied to the fatigue model as mean stress values which are incorporated into the deterministic and stochastic load ranges. 14 of 19 American Institute of Aeronautics and Astronautics
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  Appendix B: DesignFlow for Main Shaft and Bearing System1 Flowchart for DriveSE shaft and bearing model without fatigue Torque, rotor aerodynamic forces & moments, rotor & drivetrain weight, bedplate tilt angle Calculate von Mises stress of main shaft Calculte shaft diameters based on shaft von Mises stress and allowable safety factor Allowable safety factor for shaft & material Meet bearing deflection requirements? Bearing types Calculate shaft deflection No Yes Shaft geometry finalized Assume shaft length & bearing locations Calcuate bearing loads & moments Select bearings from database based on shaft geometry & carried loads Allowable safety factor for bearings Update shaft length Bearing geometry matches shaft geometry? No Yes Update shaft geometry Shaft/bearing unit design complete 15 of 19 American Institute of Aeronautics and Astronautics
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  Flowchart for DriveSEshaft and bearing model with fatigue Turbine Inputs and Shaft Size from Main Shaft Model Define Stochastic Loading Cycles Across Turbine Lifetime Calculate Deterministic Mean Loads Calculate Deterministic Alternating Loads Resolve into Deterministic Alternating Stress at Bearing Locations Resolve into Deterministic Mean Stress at Bearing Locations Resolve into Stochastic Alternating Stress at Beating Locations Define Equivalent Zero-mean Deterministic Stress Define Equivalent Zero-mean Stochastic Stress Range S-N Relationship of High-strength Steel Sum Fatigue Effects Across Turbine Life (Miner’s Rule) Damage Results in Failure? Yes No Increase Shaft Diameter Calculate Axial and Radial Forces Experienced During Lifetime Resolve into Equivalent Loads Integrate Bearing Life Consumed Across Revolution Lifetime Bearing Data Table Calculate Required Dynamic Load Rating Select Smallest Bearing Subject to Load Rating and Bore Diameter Constraints Update Shaft Size to Match Bearing Bore and Face Width Fatigue-driven Design of Shaft And Bearing(s) Complete Bearing Routine Bearing Types 16 of 19 American Institute of Aeronautics and Astronautics
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  Appendix C: Materialsand Raw Outputs in Main Shaft Materials Analysis SAE Steel Grade Condition E (Gpa) Sut (Mpa) b 1006 As-received 206 318 -0.13 1018 As-received 200 354 -0.11 1020 As-received 186 392 -0.12 1030 As-received 206 454 -0.12 1035 As-received 196 476 -0.11 1045 As-received 216 671 -0.11 1045 QT* 206 1343 -0.07 1045 QT 206 1584 -0.06 1045 QT 206 1825 -0.08 1045 QT 206 2240 -0.1 4142 QT 206 1412 -0.08 4142 QT 206 1757 -0.08 4142 QT 200 2445 -0.08 4340 As-received 192 825 -0.1 4340 QT 200 1467 -0.09 950X As-rolled 206 438 -0.1 960X As-rolled 206 480 -0.09 980X As-rolled 206 652 -0.09 1141 Normalized at 1650 F 216 771 -0.097 1141 Reheat, QT 227 925 -0.066 1141 Normalized at 1650 F 220 695 -0.096 1141 Reheat, QT 217 802 -0.079 1141 Normalized at 1650 F 214 725 -0.102 1141 Reheat, QT 215 797 -0.086 1141 Normalized at 1750 F 220 789 -0.103 1038 Normalized at 1650 F 201 582 -0.107 1038 Cold size/form 219 652 -0.098 1038 Reheat, QT 219 649 -0.097 1541 Normalized at 1650 F 205 783 -0.135 1541 Cold size/form 205 906 -0.083 1050 Normalized at 1650 F 211 821 -0.126 1050 Hot forge, cold extrude 203 829 -0.075 1050 Induction through-hardened 203 2360 -0.109 1090 Normalized at 1650 F 203 1090 -0.091 1090 Hot form, accelerated cool 203 1388 -0.106 1090 Hot form, QT 217 1147 -0.12 1090 Hot form, austemper 203 1251 -0.12 1090 Hot form, accelerated cool 203 1124 -0.093 * QT= Quenched and Tempered 17 of 19 American Institute of Aeronautics and Astronautics
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  Acknowledgments This work wouldnot be possible without the efforts of the Systems Engineering group at the National Wind Technology Center. Thanks especially to Katherine Dykes, who has supported the modeling efforts since she first began this project. The full WISDEM model set, of which DriveSE is a part, would not exist without her exhaustive efforts. Thanks also to Rick Damiani for his comprehensive industry insight. Last but not least, thanks goes to Ryan King, who has been available to answer questions and troubleshoot modeling errors from the beginning. References 1Guo, Y.; Parsons, T.; King, R.; Dykes, K.; Veers, P. ”An Analytical Formulation for Sizing and Estimating the Dimensions and Weight of Wind Turbine Drivetrain Components,” National Renewable Energy Laboratory, NREL/TP: 5000-63008, 2015 (to be published). 2King, R.; Guo, Y.; Parsons, T.; Dykes, K. (2014). ”A Systems Engineering Analysis of 3-point and 4-point Wind Turbine Drivetrain Configurations.” National Renewable Energy Laboratory. 3Jonkman, J. FAST ”An aeroelastic computer-aided engineering tool for horizontal axis wind turbines,” Software Package, ver. 7, National Renewable Energy Laboratory, Boulder, CO, URL: https://nwtc.nrel.gov/FAST7 [cited 31 March 2015]. 4Hayman, G. MExremes, ”A MATLAB-based Generator of Extreme-Event Tables,” Software Package, Ver. 1.00, National Renewable Energy Laboratory, Boulder, CO, URL: https://nwtc.nrel.gov/MExtremes [cited 31 March 2015]. 5(1992). DS 472: Loads and Safety of Wind Turbine Construction. 1st ed. Danish Standard Foundation. 6S. Frandsen, N. J. Tarp-Johansen, E. Norton, K. Argyriadis, B. Bulder, and K. Rossis. Recommendations for design of offshore wind turbines. Technical Report ENK5-CT-2000-00322, March 2005. 7H. J. T. Kooijman, C. Lindenburg, D. Winkelaar, and E. L. van der Hooft. DOWEC 6 MW pre-design. Technical Report DOWEC-F1W2-HJK-01-046/9, Energy Research Center of the Netherlands (ECN), September 2003. 8Jonkman, J. ”Dynamics of offshore floating wind turbines-model development and verification.” Wind Energy, 12(5):459492, July 2009. 9Resor, B. ”Definition of a 5MW/61.5m wind turbine blade reference model.” Sandia Report SAND2013-2569, Sandia National Laboratories, April 2013. 10Jonkman, J; Butterfield, S.; Musial, W.; Scott, G. ”Definition of a 5-MW reference wind turbine for offshore system development.” NREL/TP-500-38060, National Renewable Energy Laboratory, February 2009. 11Dykes, K.; Platt, A.; Guo, Y.; Ning, N.; King, R.;Parsons, T.; Petch, D.; Veers, P. ”Effect of Tip-Speed Constraints on the Optimized Design of a Wind Turbine.” National Renewable Energy Laboratory, October 2014 12Malcolm, D.J.; Hansen, A.C. ”WindPACT Turbine Rotor Design Study” NREL/SR-500-32495, June 2000-June 2002 13Link, H.; LaCava, W.; van Dam, J.; McNiff, B.; Sheng, S.; Wallen, R.; McDade, M.; Lambert, S.; Butterfield, S.; Oyague, F. ”Gearbox reliability collaborative project report: findings from phase 1 and phase 2 testing.” NREL/TP-5000-51885, 2011. 14Oyague, F. ”Gearbox Reliability Collaborative GRC 750 / 48.2 Description and Loading Document (IEC 61400-1 Class IIB).” rev. 3.0 NREL 2010. 15IEC (2005). 61400-1, Design Requirements for wind turbines. International Electrotechnical Commission. 16Dykes, K.; Ning, S. A.; Graf, P.; Scott, G.; Guo, Y.; King, R.; Parsons, T.; Damiani, R.; Fleming, P. The Wind-Plant In- tegrated System Design and Engineering Model, National Renewable Energy Laboratory, URL: https://nwtc.nrel.gov/WISDEM [cited 30 March 2015]. 17Gundtoft, S. ”Wind Turbines.” University College of Aarhus. 2009. 18Roessle, M.L.; Fatemi, A. ”Strain-controlled fatigue properties of steels and some simple approximations.” International Journal of Fatigue 22 (2000) 495511 19Tartaglia, J. ”The Effects of Martensite Content on the Mechanical Properties of Quenched and Tempered 0.2%C-Ni-Cr- Mo Steels.” ASM International 1059-9495, June 2009 19 of 19 American Institute of Aeronautics and Astronautics