Description and Computer Modeling of a Ball-and-Socket Hub That Enables Teetering for Three-Bladed Wind Turbines

Transcription

1 Description and Computer Modeling of a Ball-and-Socket Hub That Enables Teetering for Three-Bladed Wind Turbines Arnold Ramsland Ramsland Technology, LLC, Franklin Ridge, Chapel Hill, NC Arnold.Ramsland@ramslandhub.com A horizontal axis wind turbine with a ball-and-socket hub is disclosed. The hub enables horizontal axis turbines with two or more blades to teeter in response to wind shear gradients. Computer modeling was done using existing and modified FAST code in order to compare the new hub design with existing designs. Results show that a three-bladed turbine with the ball-and-socket hub provides very significant reductions in out-of-plane bending loads applied to the main shaft in comparison to a three-bladed turbine with a rigid hub. Results also show that the new hub design provides significant reductions in the out-of-plane loads applied to the blades. A blade fatigue study using a rainflow counting of multi-axial torque contributions at the blade root was performed in order to assess the impact of these reductions, and results show that the three-bladed turbine equipped with a ball-and-socket, teetering hub provides for very significant reductions in lifetime blade damage in comparison to existing wind turbine designs due to a combination of factors. The first factor is that teetering largely eliminates the cyclic variations in out-of-plane torque on the blades that are observed with rigid hubs. Here, the fatigue study shows that the three-bladed wind turbine with a teetering hub provides for an approximate sixfold reduction in lifetime blade damage in comparison to a three-bladed turbine with a rigid hub. The second factor is that the addition of a third blade reduces the load on each blade by one-third. Here, the fatigue study shows that a three-bladed turbine with a teetering hub provides for an approximate fourfold reduction in lifetime blade damage in comparison to a two-bladed turbine with a teetering hub. [DOI: / ] 1 Introduction Presently, most horizontal axis wind turbines are equipped with either three blades with a rigid hub (3R) or two blades with a teetering hub (2T). The teetering hub provides for an additional degree-of-freedom (DOF) by enabling the turbine rotor to pivot back-and-forth like a playground seesaw in response to wind shear. Sources of wind shear include variation of wind velocity with height, turbulence, tower shadow, and shadow from neighboring wind turbines in a wind farm. This out-of-plane rotation, or teetering, is beneficial when there is wind shear because it eliminates the out-of-plane difference in torque between the two blades. As a result, the blades do not apply a bending torque about the teeter axis to the shaft tip as long as the teetering is unconstrained. Teetering can also impact differences in in-plane torque applied by the blades to the hub because the blade experiencing the higher wind velocity will typically move with the wind and the blade experiencing the lower wind velocity will typically move into the wind. As a result, the teetering motion of a twobladed wind turbine tends to equalize the effective wind speeds applied to the blades, thereby reducing the stresses on the blades. In contrast, the rigid hub does not balance the out-of-plane torque on the hub so that wind shear and turbulence will increase fatigue damage to the blades. Because of the advantages afforded by teetering, two bladed turbines are almost exclusively manufactured with a teetering hub rather than a rigid hub (2R). The purpose of this paper is to present a new ball-and-socket hub design (3T) that enables teetering for a three-bladed wind turbine and to present computer modeling comparing performance to Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received May 20, 2014; final manuscript received February 4, 2015; published online March 12, Assoc. Editor: Yves Gagnon. existing 3R, 2T, and 2R designs. That comparison includes fatigue analysis on the blades to determine if the benefits realized by teetering with two-bladed turbines are also realized by teetering with three-bladed turbines. The modeling was performed with a very large, upwind wind turbine, however, the ball-and-socket can be used and modeled on all sizes of horizontal axis wind turbines in either the upwind or downwind configurations. The ball-and-socket hub has been awarded a U.S. patent [1] issued in A continuation-in-part [2] was published to include transfer assemblies and modeling results. 2 Description of 3T Wind Turbine 2.1 Wind Turbine Undergoing Teetering. Figure 1 is a side image of a wind turbine equipped with the ball and socket hub. The figure shows the wind turbine undergoing teetering, where in this example, the rotations of blade 1 is backward and that of blade 3 is forward. 2.2 Ball-and-Socket Hub Design. The hub design comprises four major parts: the main shaft ball, the hub socket, transfer assemblies, and blade connectors that fit within a recess in the hub socket. These separate parts are shown in an exploded, isometric view in Fig. 2. Figure 3 shows an image of the main shaft, main shaft ball, and the outer portion of a transfer assembly. The main shaft ball is affixed to and rotates with the main shaft. For comparison, the rotations of the main shaft ball would be identical to those of a rigid hub in the 3R configuration. The main shaft ball has a series of longitudinal grooves that are centered on and uniformly distributed around an equator of the main shaft ball that is perpendicular to the x-axis, or main shaft axis. A more detailed drawing of the transfer assembly is provided in Fig. 4. The Journal of Solar Energy Engineering Copyright VC 2015 by ASME JUNE 2015, Vol. 137 /

2 Fig. 1 Wind Turbine undergoing teetering assembly comprises a coupling base, groove fitting, transfer bearings, and a pitch motor support. At the inner end of the transfer assembly is a groove fitting that fits within the longitudinal grooves on the main shaft ball. Insertion of the groove fitting portion of a transfer assembly into a longitudinal groove on the main shaft ball is shown in Fig. 3. A more detailed drawing of the hub socket is shown in Fig. 5. The hub socket comprises a series of hub socket housing connectors and a series of hub socket housings. The figure shows that the inner surfaces of the hub socket housing connectors are a portion of the surface of a sphere. The diameter of the inner spherical surface of the hub socket as shown in Fig. 5 is slightly greater than the diameter of the outer spherical Fig. 3 Alternate main shaft ball with fitted transfer assembly surface of the main shaft ball. This enables the hub socket to surround and rotate about the main shaft ball, but prevents separation of the two. The goals in the design of the ball-and-socket hub are to transfer rotational torque from the blades to the main shaft, enable teetering for three blades, and prevent that teetering from changing the pitch angle of the blades. In order to achieve these goals, limitations are placed upon the rotation of the hub socket about the main shaft ball and additional rotations are enabled within the hub socket. A typical ball-and-socket arrangement allows the socket to freely rotate about the ball across three axes, e.g., x, y, and z. In Fig. 2 Exploded view of ball-and-socket hub Fig. 4 Transfer assembly / Vol. 137, JUNE 2015 Transactions of the ASME

3 Fig. 5 Hub socket order to transfer rotational torque from the blades to the main shaft, the hub is prevented from rotating about the x-axis of the main shaft ball. This is achieved by placing the groove fittings within longitudinal grooves of the main shaft ball and placing the coupling bases and transfer bearings within the hub socket. Contact of the groove fittings with the sides of the longitudinal grooves prevents the hub socket from rotating about the x-axis, thus enabling transfer of torque from the blades to the main shaft. Teetering for three blades is achieved by enabling the hub socket to rotate about the remaining two axes of the main shaft ball and enabling the groove fittings to move within the longitudinal grooves of the main shaft ball. The longitudinal grooves establish the teetering paths for the groove fittings and blades. The teetering path of an individual blade forms an arc, where the arc is a segment of a circle constructed such that the plane of the circle (or teetering plane) is intersected by the x-axis and the various pitch axes of the blade, and the center of the circle is coincident with the center of the main shaft ball. The teetering plane and the above points and lines that are located on the teetering plane are shown in Fig. 6, where the main shaft and main shaft ball are sliced in half. In this example, the teetering limits are designed to be 610 deg with pitch axes shown at the ends of the teetering arc. The extent of teetering is limited by the dimensions of the longitudinal grooves, groove fittings, and teetering stops. Finally, the ball-and-socket hub is designed so that teetering does not result in a change in the pitch angle of the blades, however, the explanation requires the equations and figures presented in Sec Each part of the ball-and-socket hub has one or more DOF relative to the other parts. The hub socket has two rotational DOF with respect to the main shaft ball to enable rotation about the main shaft ball. The transfer assembly has 1DOF with respect to the hub socket to enable the transfer assembly to rotate within the hub socket about the pitch axis of a blade. The groove fitting has 1DOF with respect to the main shaft ball that enables rotation (or teetering) within the longitudinal groove of the main shaft ball. The blade connector has 1DOF with respect to the other parts of the ball-and-socket hub, enabling the pitch motor that is affixed to the transfer assembly to rotate the blades. Fig. 6 plane Main shaft ball showing teetering arc and teetering flexible, inner hub protector that protect the ball-and-socket hub from the environment. This protection is necessary since the hub socket and transfer assembly are in both continuous motion and continuous contact with the main shaft ball, and lubricant in the grooves and on the surface of the main shaft ball would be exposed to the environment. Presently, the role of the nose cone is principally an aesthetic adornment as described by Gipe [3], so new design concerns are needed to assure isolation of the balland-socket hub from the environment. 2.4 Working Model. A working model has been made using stereolithography to manufacture the ball-and-socket hub and blades. By allowing for a small gap (0.32 mm) between the ball and socket, it was possible to manufacture the ball-and-socket hub 2.3 Protection of Ball-and-Socket From the Environment. Figure 7 shows a view of the wind turbine with a nose cone and a Fig. 7 Wind turbine with ball-and-socket hub protected by nose cone and back protector Journal of Solar Energy Engineering JUNE 2015, Vol. 137 /

4 in a single operation. The model has three blades attached to the hub and testing confirms all teetering movements described in this paper. Pitch motors were not used in this model. 2.5 Design Comparison to 2T. The 2T and 3T configurations would require many of the same considerations in design and operation. Examples include means for limiting teetering and a design that eliminates the possibility of tower strikes. A recent paper by Schorbach et al. [4] investigates teeter end impacts. If the ball-and-socket hub were equipped with two blades, the teetering profile would be identical to that of a 2T configuration. 3 Computer Modeling Computer modeling was performed to compare the performance of the 3T turbine with existing 2R, 2T, and 3R turbines using software tools available from NREL (National Renewable Energy Laboratory). Wind turbine modeling was performed using FAST [5] (Fatigue, Aerodynamics, Structures, and Turbulence) code to predict power generation and fatigue loads on the various components of a wind turbine. The modeling is based upon blade element momentum theory. The wind turbine used for study was the onshore configuration of the hypothetical, 5-MW wind turbine [6] developed by NREL for the International Offshore Code Comparison Collaboration (OC3) [7]. Wind profiles were generated using Turbsim [8] so that comparisons could be made according to IEC standards [9] with tower shadow and turbulence taken into account. Fatigue analysis of the blades was performed using MLife [10], which is a tool developed by NREL to postprocess results from FAST and compute statistical information and fatigue estimates. 3.1 Coordinate Systems. FAST software uses nine coordinate systems as indicated in the FAST User s guide [5]. In this paper, only the shaft (s) and the azimuth (a) coordinate systems are described. Both coordinate systems are aligned with the main shaft so that the x s and x a axes are identical and both can be designated as the x-axis, or main shaft axis. The coordinate systems differ in that the shaft coordinates remain fixed whereas the azimuth coordinates rotate with the rotor. Results were also reported by FAST using the rotating cone coordinate system (c), however, since the precone angle was set to 0 deg, the cone and azimuth coordinate systems are identical. For this reason, the cone coordinate system is not described. existing code determine the rotation angle (Rot_ya), rotation velocity (RotV_ya), and rotation acceleration (RotA_ya). Almost identical copies of these sections were added in the modified code in order to determine the rotation angle (Rot_za), rotation velocity (RotV_za), and rotation acceleration (RotA_za) about the z a axis. 4.3 Determination of Individual Teetering Rotations. The FAST code also requires teetering angles and velocities of each individual blade for various calculations. By knowing the teetering angles and velocities about the y a and z a axes as described in Sec. 4.2, the teetering rotations for blades 1, 2, and 3 are determined according to the following equations: Teeter Rotation Blade 1 ¼ Rot ya (1) Teeter Rotation Blade 2 ¼ sinð330 degþrot ya þ cosð330 degþrot za (2) Teeter Rotation Blade 3 ¼ sinð210 degþrot ya þ cosð210 degþrot za (3) where blades 1, 2, and 3 are positioned at 90 deg, 330 deg, and 210 deg, respectively. The same approach is used to calculate the teeter angular velocities for blades 1, 2, and 3. Here, the angular rotational velocities about the y a and z a axes are designated RotV_ya and RotV_za, and the teeter angular velocities for the blades are determined by the following equations: Angular Velocity Blade 1 ¼ RotV ya (4) Angular Velocity Blade 2 ¼ sinð330 degþrotv ya þ cosð330 degþrotv za (5) Angular Velocity Blade 3 ¼ sinð210 degþrotv ya þ cosð210 degþrotv za (6) The y a and z a axes are imaginary axes used by FAST code to enable two independent rotations. The choice of the orientation of these axes was based upon minimizing changes to FAST code, however, any orientation of perpendicular y a and z a axes could have been 4 Modifications to Source Code 4.1 Additional DOF. In order to assess the performance of three-bladed turbines with teetering enabled, computer modeling was performed by modifying FAST (Version 7.2). The present FAST software code [5] can model turbines with two or three blades. Two-bladed turbines can be modeled with teetering either enabled or disabled, whereas three-bladed turbines do not permit teetering. The present FAST code enables teetering of two-bladed turbines by having a DOF (tdofya) to balance differences in outof-plane torque about the y a axis as shown in Fig. 8. The y a is also the axis of the teeter hinge (or pin) and rotates with the hub about the x-axis. Figure 8 also shows z a, the pitch axis of blades 1 and 2. In adapting this DOF to a hub with three blades, the y a axis remains unchanged from present software with respect to blade 1 so that blade 1 continues to teeter about the y a axis against a combination of blades 2 and 3. The code was further modified by adding a second DOF, tdofza, to enable blades 2 and 3 to teeter against one another about the z a axis. The orientations of y a and z a axes for three-bladed turbines are shown in Fig Determination of Rotations About the y a and z a Axes. The out-of-plane rotation of the hub socket about the y a axis is determined by the existing FAST code. Various sections of the Fig. 8 Teetering and pitch axes of two-bladed wind turbine / Vol. 137, JUNE 2015 Transactions of the ASME

5 Fig. 9 Teetering and pitch axes of three-bladed wind turbine chosen. Examination of the above equations shows blades 2 and 3 rotating about both axes and the calculations for teetering rotation and angular velocity include contributions from each. Teetering about a combination of two imaginary axes can equivalently be expressed as teetering about a single axis where that teetering axis is perpendicular to the orientation of the blade as shown in Fig. 9. As discussed in Sec. 2.2, the teetering path is defined by the longitudinal grooves, so the teetering axes shown in Fig. 9 are the actual teetering axes. Summing the above equations for both teeter deflections and teeter angular velocities of blades 1, 2, and 3 gives a value of zero. Although three blades teeter, there are only 2DOF since subtracting the teetering angles (or angular velocities) of any two blades from zero determines the teetering angle (or angular velocity) of the remaining blade. This is shown in the example provided in Fig. 2, where entering values of 5 deg and 4 deg for Rot_ya and Rot_za into Eqs. (1) (3) gives teetering rotations of blades 1:2:3 equal to 5.00 deg: 0.96 deg:5.96 deg. 4.4 Pitch Angle Rotations of Hub Socket. As described in Sec. 2.2, teetering for three blades is achieved by enabling the hub socket to rotate about the remaining two axes of the main shaft ball, e.g., y a and z a. As a result, the hub socket follows the teetering rotations of the blades, so if blades 2 and 3 teeter against one another about the z a axis, the hub socket rotates about the z a axis. As shown in Fig. 9, the z a axis is also the pitch axis of blade 1, so the teetering angle between blades 2 and 3 about the z a axis would also be the rotation angle of the hub socket about the pitch axis of blade 1. Figure 2 also shows the pitch axes of blades 1 and 2 at the center the respective transfer assemblies. These hub socket rotations (HSR) about the pitch axes of blades 1, 2, and 3 that are due to the teetering of the remaining two blades can be determined according to the following equations: HSR about Blade 1 pitch axis ¼ Rot za (7) HSR about Blade 2 pitch axis ¼ cosð330 degþrot ya þ sinð330 degþrot za (8) HSR about Blade 3 pitch axis ¼ cosð210 degþrot ya þ sinð210 degþrot za (9) A rotation of the hub socket about the pitch axis of a blade would not change the teetering angle of that blade, however, it would change its pitch angle if the blades completely matched the pitch rotations of the hub socket. In this case, these pitch rotations would change the desired pitch rotation and would have to be included in the FAST code. In the above example, entering 5 deg and 4 deg for Rot_ya and Rot_za into Eqs. (7) (9) gives pitch rotations of blades 1:2:3 equal to 4.00 deg: 2.33 deg:6.33 deg. These pitch rotations would likely have a negative impact upon power production because the pitch angles would no longer be at the optimal values. These pitch rotations would also possibly cause undesirable dynamical effects because teetering leads to an increase in the pitch angle differences between blades, and this increase in turn leads to an increase in teetering. Pitch rotations are prevented by adding a transfer assembly to the ball-and-socket hub as described in Sec. 2.2, so that the blades rotate with the transfer assembly rather than the hub socket. A transfer assembly is prevented from following the pitch rotations described above because the groove fitting is prevented from rotating about the pitch axis due to contact with the longitudinal grooves. By allowing the transfer assemblies to rotate within the hub socket about the respective pitch axes of the blades, any potential pitch rotation caused by the HSR is met with an equal and opposite pitch rotation of the transfer assembly and blades. Combining the two equal and opposite rotations gives a net pitch rotation of the transfer assemblies and blades (relative to the orientation of the main shaft) equal to zero, so modifying the FAST code to include pitch rotations caused by teetering is not necessary. 4.5 Modification to User Teetering Subroutine. The present code allows for spring(s) to control the teetering of blades 1 and 2 in two-bladed turbines. Teetering can be constrained using a soft spring with a relatively small spring constant and/or a hard spring with a very high spring constant. The code was modified by adding separate spring(s) to blades 1, 2, and 3 in the UserTeet subroutine. To simplify matters, the spring constants for blades 1, 2, and 3 were made equal to each other. Parameters were set so that a soft spring ( N m/rad) was engaged at 68 deg, and a hard spring ( N m/rad) was engaged at 610 deg. This would be consistent with stops as shown in Fig. 3 where springs of different lengths are placed in the interior of the stops such that soft springs would engage at 68 deg and hard springs at 610 deg. 4.6 Summary of Changes to FAST Code. The modifications to the FAST code are straightforward due to the organized structure of the code and the guidance provided by the existing calculations related to teetering and numerous comment statements. The major modifications to the FAST code that enables teetering for three blades include the addition of a new DOF (tdofza) that enables determination of rotations about the z a axis and determination of teetering rotations for blades 1, 2, and 3. Some additional minor changes are necessary, however, these minor changes are best viewed by examination of the modified FAST code. For this reason, all changes in code are documented with comment statements. 4.7 Modification of Pitch Control Routine (discon.dll). The 5-MW wind turbine uses a dynamic link library, discon.dll, to control the pitch of the blades in order to maintain the generator power output at 5 MW when wind velocity exceeds the rated limit. It was desired to also provide additional values of rated power in order to provide better comparisons of two and threebladed turbines and also to investigate the impact of changing power upon blade fatigue. The appropriate constants in the discon.f90 source code were modified and the code recompiled to change the rated power of 5 MW to other values (5.6 MW and 7.5 MW). The constants (maximum torque rate, maximum generator torque, and rated generator power) were modified by multiplying by the rated power ratio, e.g., 5.6/5. 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6 5 Methodology 5.1 Wind Turbine. The study was performed using the onshore configuration of the hypothetical 5-MW wind turbine with parameters presented in Table 1. Parameter Table 1 5-MW wind turbine properties Value/file Rating 5 MW Rotor orientation Upwind Configuration 3 blades Control Variable speed, collective pitch Drive train High-speed, multiple-stage gearbox Rotor diameter 126 m Hub height 90 m Cut-in, rated, cut-out wind speed 3 m/s, 11.4 m/s, 25 m/s Cut-in, rated rotor speed 6.9 rpm, 12.1 rpm Rated tip speed 80 m/s Blade mass 17,749 kg Rotor mass 110,000 kg Rotor inertia 38,832,896 (kg m 2 ) Nacelle mass 240,000 kg Tower mass 347,460 kg 5.2 FAST. The onshore configuration was used for analysis. Parameters and files used are listed in Table 2. The two-bladed wind turbine was created by changing the number of blades from three to two in the FAST input file. In so doing, the rotor mass and rotor inertia are reduced to 92,260 kg and 25,927,238 kg m 2, respectively. No changes were made to any other parameters. The purpose in making the change in this way was to leave all blade parameters unchanged, however, as indicated by Burton et al. [11], comparison of two and three-bladed turbines is very difficult because it is not possible to establish equivalent designs. Parameter Table 2 FAST modeling parameters and files Value Number of blades 2 and 3 Tstart, Tmax (s) 10,760 Integration time step (s) 0.05 Reporting time step (s) 0.5 Overhang, 5m, 5 deg, 0 deg shaft tilt, precone Yaw control None Pitch control Discon.dll Blade NRELOffshrBsline5MW_Blade.dat Aerodyn AeroDyn_TowerInfl.ipt Adams NRELOffshrBsline5MW_ADAMSSpecific.dat Linearization NRELOffshrBsline5MW_Linear.dat Tower NRELOffshrBsline5MW_Tower_Onshore.dat Tower shadow model Newtower Tower drag AeroDyn_Tower.dat 5.3 Wind Profile. Turbsim was used to generate a series of wind profiles as summarized in Table 3. Values not indicated were not changed from the default setting. Two profiles were generated for each mean wind speed using normal turbulence for a class A wind type. 5.4 Fatigue Study. The literature provides for various physical and computer modeling approaches to determine fatigue on wind turbine blades. Physical fatigue testing at facilities such as the Wind Technology Testing Center in Massachusetts and Knowledge Center WMC in the Netherlands perform accelerated fatigue testing. Computer modeling approaches generally rely upon physical testing data to determine the necessary parameters for determination of blade fatigue. An example of developmental work in blade fatigue is provided in a paper by Epaarachchi and Clausen [12]. A summary of work done by various authors is provided by Vassilopoulos [13]. Fatigue studies on the NREL 5-MW wind turbine were also performed by Etemaddar et al. [14] and Lee et al. [15]. The paper by Lee focused on atmospheric and wake turbulence impacts on blade and tower fatigue, and the paper by Etemaddar focused upon the impact of pitch controller faults upon blade fatigue. Although these two studies used the same 5-MW wind turbine presented in this paper, neither provided a value for the ultimate design load for the blades (L ult ) that is needed to perform lifetime fatigue damage studies (see Sec. 6.5). To address this lack of information, a strategy was used to estimate this value by assuming that wind turbine blades provided by the NREL 5 MW, 3R wind turbine have a 20-yr lifetime. In order to perform blade fatigue calculations for other configurations, the same parameters and experimental conditions that established 20 yr to failure for the 3R turbine were used to calculate the number of years to failure for the 3T, 2T, and 2R turbines. In the case of two-bladed wind turbines, the power generation would obviously be decreased if the only change was removal of the third blade. For this reason, the generator power was increased from 5.0 to 5.6 MW in order to achieve approximately the same lifetime power generation. The fatigue study was carried out by using MLife [10] to analyze the FAST output files. This software follows the techniques outlined in Annex G of IEC edition 3, where fatigue damage due to fluctuating loads is broken down into individual hysteresis cycles. The local minima and maxima of these cycles are matched by means of a rainflow counting technique developed by Matsuishi and Endo [10,16]. MLife then calculates the blade fatigue using techniques developed by Palmgren [17] and Miner. The damage is determined using Miner s rule [18], where each cycle contributes a fraction of the total damage. The contributions are added together, and failure occurs when the sum of the fractions reaches unity. A thorough documentation of all equations used for calculation of fatigue is presented in the MLife Theory Manual [10]. 5.5 Multi-Axial Torque and Fatigue. Fatigue was determined by combining torque contributions about all axes using the approach described by Bannantine and Socie [19], where cycles were counted on various planes and the critical plane was determined to be the one experiencing the greatest amount of fatigue damage. In adapting these techniques to fatigue about the blade root, the torque contributions about the three axes at the blade root were mathematically combined to determine the blade damage at each h. The value of h that caused the most damage (and shortest time to failure) was designated h max and the torque value, Mh max. During evaluation, it was found that the fatigue damage about the z c axis is negligible in comparison to the damage about the x c and y c axes so the contribution about the z c axis is omitted. Combining the torque fractions about the x c and y c axes for each blade n gives the following equation for the torque contribution about an axis h [20]: Mh ¼ cosðþrootmxc h þ sinðþrootmyc h (10) All values of h from 0 deg to 180 deg were used for determination of Mh and the torque value that generated the maximum fatigue between 0 deg and 180 deg is defined as Mh max. Since the value for Mh is determined for each blade (e.g., Mh 1 ), the angle that provided the maximum fatigue for all blades is designated h max. The individual values of lifetime damage and time to failure for each blade are averaged at h max and used for comparison of the blade fatigue in the 2R, 2T, 3R, and 3T wind turbines. The value of 10 chosen for the W ohler exponent was also used by / Vol. 137, JUNE 2015 Transactions of the ASME

7 Etemaddar et al. [14] who indicated that this value is appropriate for the composite material used in wind turbine blades. Figure 10 shows the binned Weibull wind distribution using the parameters in Table Lifetime Mean Power. Finally, a visual basic program was developed to calculate the lifetime mean power generation for each turbine configuration using MLife [10] summary files. The lifetime mean power generation was calculated by applying the fraction of time spent in each wind speed bin as provided in the Lifetime file to the mean generator power for each wind speed bin as provided in the Statistics file. 6 Results and Discussion Comparison of wind turbines with rigid and teetering hubs is provided graphically and quantitatively. FAST results for the graphical presentations were obtained using the parameters described in Table 3 for one of the files generated with a mean wind speed of 12 m/s. A representative time frame of s was used for all comparisons, except Fig. 17 which shows a spike in output between 500 and 600 s. A limited time span of 100 s was chosen in order to better show possible cyclic variability in output. 6.1 Comparison of Two and Three-Bladed Teetering. Figures 11 and 12 show blade 1 teetering deflections for two and three-bladed wind turbines. The figures show generally comparable profiles. Also, FAST provides output of tower clearance for 2T and 3T and at no time was this value less than zero (which would indicate a tower strike). 6.2 Comparison of Out-of-Plane Bending Torque Applied to Low-Speed Shaft. The impact of changing the source code to enable rotation of blades about y a and z a axes can be seen by examination of the out-of-plane bending torque applied by the rotor to the low-speed (or main) shaft tip about the y a and z a axes (designated LSSTipMya and LSSTipMza by FAST). It is expected that these values would be zero because physical testing with the working model shows it is not possible for the ball-and-socket hub to transfer bending torque to the low-speed shaft (LSS) unless the teetering stops are reached. Figures 13 and 14 show a comparison of these output measures for three-bladed wind turbines with rigid and teetering hubs. Both figures show that this bending torque is significant for the rigid hub and virtually zero for the teetering hub. It would also be expected that LSSTipMya would also be zero for a 2T wind turbine because teetering occurs about the y a axis. This expectation is confirmed as shown in Fig. 15. In contrast, teetering does not occur about the z a axis so LSSTipMza should not be affected. Figure 16 shows that LSSTipMza is somewhat greater for the 2T hub than the 2R hub, although the values are considerably less than LSSTipMza with the 3R wind turbine. A visual examination of all plots of LSSTipMya and LSSTipMza for the 3T turbine was performed for the entire analysis time (750 s) on all FAST output files using parameters listed in Table 3. Examination showed that at the higher wind speeds (> ¼ 24 m/s), the teetering stops were reached approximately once per file. When teetering stops are reached, short-term spikes in LSSTipMya and/or LSSTipMza are observed. Figure 17 shows the output for LSSTipMya output from a wind profile with a mean wind speed of 30 m/s. The figure shows a spike at 557 s that occurs when the stops are engaged. Otherwise, LSSTipMya and LSSTipMza were close to zero over the entire analysis time. Since the blade fatigue study includes all data, the impact of blades hitting the teetering stops is included in the estimate of the lifetime blade damage. 6.3 Reduction in Loads Applied to the Main Shaft Bearing. Computer modeling shows that the ball-and-socket hub provides very significant reductions in the out-of-plane loads applied to the main shaft bearings. Figures 18 and 19 show comparisons of bending moments about the main shaft s strain gage. The main shaft bearing would be subject to these moments about the stationary y s and z s axes since it is placed at the location of the main shaft s strain gage. Additionally, it would be expected that a portion of these loads would pass onto the gearbox. A paper by Fleming et al. [21] reported that conversion of a 2T hub to a 3R hub resulted in an unstable 2.7 Hz drivetrain oscillation at rated speed (generator, high-speed shaft (HSS), LSS torsion, and edgewise blade bending). The paper did provide possible causes of these vibrations, however, it is also possible that the transfer from a teetering hub to a rigid hub played a role since teetering reduces the bending moments applied to the LSS. 6.4 Comparison of In-Plane and Out-of-Plane Bending Torque Applied to Blade Root. Figure 20 shows that in-plane torque applied to the blade root (RootMxa1) is comparable for the rigid and teetering hubs. In contrast, Fig. 21 shows significant differences between the 3T and 3R wind turbines for the out-ofplane bending torque applied to the blade root (RootMya1). The figure shows that the two hubs have approximately the same moving average, however, the rigid hub shows an added cyclic variability not seen with the teetering hub. Comparison of out-ofplane torque for the rigid hub as shown in Fig. 21 with the bending torque at the shaft tip as shown in Fig. 13 shows the cyclic variability in torque at the blade root generally correlates with the cyclic variability in bending torque at the shaft tip. Figure 13 also shows that this bending torque at the shaft tip for the 3T hub is Table 3 Parameter Turbsim parameters used for wind profile generation Value(s) Mean wind speeds (m/s) 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 Turbulence model IECKAI (Kaimal) IEC standard ED3 (large, onshore) Turbulence characteristic NTM (normal) IEC wind type A IEC wind turbine class 1 Vertical mean flow (uptilt) angle 0 deg Horizontal mean flow (skew) angle 0 deg Grid matrix dimensions Grid height, grid width (m) Random seed Unique for each profile Analysis time, usable time 800 s, 760 s Fig. 10 Lifetime Weibull wind speed distribution Journal of Solar Energy Engineering JUNE 2015, Vol. 137 /

8 Table 4 damage MLife parameters used for determination of lifetime Blade 1 fatigue channels Blade 1 calculated fatigue channels Blade 2 fatigue channels Blade 2 calculated fatigue channels Blade 3 fatigue channels (if applicable) Blade 3 calculated fatigue channels RootMxc1, RootMyc1, RootMzc1 Mh 1, h ¼ 0 deg to 180 deg, step 10 deg RootMxc2, RootMyc2, RootMzc2 Mh 2, h ¼ 0 deg to 180 deg, step 10 deg RootMxc3, RootMyc3, RootMzc3 Mh 3, h ¼ 0 deg to 180 deg, step 10 deg Design life 20 yr (631,150,000 s) Availability 100% Weibull shape 2 Weibull scale (mean wind speed) Cut-in, cut-out wind speed (m/s) 3, 25 Maximum wind speed (m/s) 31 Wind speed bin size (m/s) 2 10 m/s Multiplier for binning 0.5 unclosed cycles Design load case Power production (IEC DLC 1.2) Goodman correction Yes Data filtering No W ohler exponent 10 Fig. 13 Rotating bending moment at LSS tip about y a axis with three-bladed hub (LSSTipMya) Fig. 11 Blade 1 teetering profile with three-bladed hub Fig. 14 Rotating bending moment at LSS tip about z a axis with three-bladed hub (LSSTipMza) Fig. 12 Blade 1 teetering profile with two-bladed hub Fig. 15 Rotating bending moment at LSS tip about y a axis with two-bladed hub (LSSTipMya) / Vol. 137, JUNE 2015 Transactions of the ASME

9 Fig. 16 Rotating bending moment at LSS tip about za axis with two-bladed hub (LSSTipMza) Fig. 19 Nonrotating low-speed shaft bending moment about zs axis at the shaft s strain gage (LSSGagMzs) Fig. 17 Rotating bending moment at low-speed shaft tip about ya axis with three-bladed hub (LSSTipMya) showing spike with teetering hub Fig. 20 In-plane bending moment at blade 1 root (RootMxc1) Fig. 18 Nonrotating low-speed shaft bending moment about ys axis at shaft s strain gage (LSSGagMys) Fig. 21 Out-of-plane bending moment at blade 1 root (RootMyc1) Journal of Solar Energy Engineering JUNE 2015, Vol. 137 /

10 Table 5 Lifetime damage fractions based upon torque about x a and y a axes Hub Rated power (MW) Mxa1 Mya1 Mxa2 Mya2 Mxa3 Mya3 3R T R T R T R T nonexistent, strongly suggesting that teetering largely eliminates the cyclic variability in out-of-plane torque at the blade root as shown in Fig Fatigue Comparison of Teetering and Rigid Hubs. The impact of this cyclic variability in torque has been determined by using MLife to perform fatigue analysis on the blades. In using MLife, it is necessary to provide L ult, the ultimate design load of the blade. The value of L ult is dependent on the design and materials used for manufacture of the blade. Since this value is unknown for the 5-MW blade, a trial-and-error approach was used to determine what value of L ult would be necessary in order for a 3R wind turbine to have a design life of 20 yr using the parameters in Table 4. Choosing the value of Mh max that provided a lifetime damage equal to one and a time to failure equal to 20 yr resulted in L ult equal to 38,205 kn m. This value of L ult was also used for twobladed wind turbines because the same blades were used. Since the mean lifetime power for a two-bladed wind turbine with 5 MW rated power is less than that of a three-bladed 5-MW turbine, the rated power was increased to 5.6 MW for better comparison to three-bladed turbines. Fatigue values at 5 MW are also provided for comparison. The data in Table 5 show significant differences between the teetering hubs and rigid hubs regarding in-plane and out-of-plane blade damage. The most significant parameter for rigid hubs is the out-of-plane torque, Myan (n ¼ 1,2, ). Choosing results from blade 1 data show that the damage fraction ratios are / or 39.4 times greater for the 3R than 3T and / or 9.1 times greater for the 2R than 2T. The most significant parameter for teetering hubs is the in-plane torque, Mxan. Data show that the damage fraction ratios are / or 2.6 times greater for 3T than 3R and / or 4.7 times greater for 2T than 2R. Overall, however, the teetering hubs show considerably less lifetime damage fatigue when comparing the values of 2T and 3T about the x a axis with the respective values of 2R and 3R about the y a axis. The data also show that teetering provides at least as much benefit to a three-bladed turbine as it does to a two-bladed turbine. The data in Table 6 show an exceptional advantage for the 3T turbine in comparison to all other turbines. The damage ratio (1.0004/0.1647) for 3R compared to 3T shows that the lifetime damage is 6.1 times greater for 3R. Additionally, the damage ratio (0.6460/0.1647) for 2T compared to 3T shows that the lifetime damage is 3.9 times greater for 2T. The very significant reduction in fatigue for the 3T wind turbine is due to a combination of factors that are evident by examining results from the existing hub designs. The first factor is that each blade in a two-bladed turbine generates 1.5 times the power compared to a three-bladed wind turbine, and blade damage increases at a much greater rate than mean power as seen by comparing values of 3R at 5.0 and 7.5 MW as described in Sec The second factor is that teetering very significantly reduces lifetime blade damage. This is seen by comparing the blade damage for the twobladed turbines with rigid and teetering hubs. At 5.0 MW, the lifetime damage ratio of the 2R to 2T is / or Hence, combining these two factors with a 3T hub provides the basis for the very significant reduction in lifetime blade damage. 6.6 Increase in Mean Lifetime Power. An important consequence of reducing blade fatigue is that it allows for an increase in the mean lifetime power. An example of the impact of increasing power on blade damage is seen with the 3R wind turbine. Increasing the rated power from 5.0 to 7.5 MW increases the mean lifetime power by 25.8%, but also increases the lifetime blade damage by 262%. If, however, the increase in rated power is combined with a substitution of a teetering hub for the rigid hub, the mean lifetime power is increased by 24.9% while the lifetime blade damage is decreased by 70.3%. Table 6 Lifetime damage based upon multi-axial torque Hub Rated power (MW) h max Mean power (MW) Output using Mh max Blade 1 Blade 2 Blade 3 Blade mean 3R deg Lifetime damage Years to failure T deg Lifetime damage Years to failure R deg Lifetime damage Years to failure T deg Lifetime damage Years to failure R deg Lifetime damage Years to failure T deg Lifetime damage Years to failure R deg Lifetime damage Years to failure T deg Lifetime damage Years to failure Note: The FAST output parameters have been shortened by eliminating the prefix Root. The lifetime damage values for RootMzc1, RootMzc2, and RootMzc3 are all negligible (<10 17 ) / Vol. 137, JUNE 2015 Transactions of the ASME

11 6.7 New Blade Design Options. Another consequence of teetering is that it opens new options for design of blades for threebladed wind turbines. As shown in Table 5, the most important concern for turbines with rigid hubs is out-of-plane torque whereas the most important concern for teetering hubs is in-plane torque. Since the impact of gravity on blade mass is a very significant portion of in-plane torque on the blade, reducing blade mass will provide a greater reduction in fatigue for blades attached to the ball-and-socket hub than to the rigid hub. By combining the observed lower fatigue of 3T blades as seen in Table 6 with the predicted significant benefit afforded by reducing the blade mass, it is quite possible that teetering blades for a 3T wind turbine can be made lighter and more cheaply. This possibility is supported with a chart provided by Arimond in an article edited by Dvorak [22] showing that the power to weight ratios of blades in twobladed, teetering turbines are generally greater than the ratios of blades in three-bladed, rigid hub turbines. 6.8 Support of Increasing Power Generation. An ongoing trend in wind turbine design is the increase in size of the blades and the corresponding increase in rated power. In response to this trend, new blade designs and materials are continually being developed. Since blade fatigue increases at a much greater rate than power generation, it is likely that at some point, it will not be possible to manufacture a blade having an ultimate design load capable of supporting the desired rated power. The present fatigue study shows that this design limit will occur much sooner with current 2T and 3R wind turbines than with the 3T wind turbine. 7 Conclusion Evaluation of the computer modeling data for loads on the main shaft and main shaft bearing for a 3T turbine is very considerably less than these loads with a 3R turbine. Evaluation of the blade fatigue study reveals that a ball-andsocket hub equipped with three blades provides for a very significant reduction in blade damage and that this reduction is partially predictable by extrapolation of trends shown with other wind turbine configurations. The first trend from the blade fatigue study is that teetering provides for very significant reduction in lifetime blade damage. This significant reduction can be seen with existing turbines by comparing 2T and 2R wind turbines. A second trend is that adding an additional blade significantly reduces blade fatigue as seen by comparing 3R and 2R wind turbines. A 3T wind turbine provides for an extrapolation of these trends by combining the benefits of teetering with the benefits of having three blades. As a result, a 3T wind turbine provides for very significant reductions in blade damage in comparison to 2R, 2T, and 3R wind turbines. A final conclusion is that enabling teetering for a threebladed turbine provides for at least the same benefit in reducing blade fatigue as does enabling teetering for a two-bladed turbine. 8 Next Steps Future work includes both short- and long-range goals. It is anticipated that short-range steps can be performed readily using existing resources whereas the long-range goal will likely require assistance and additional resources. 8.1 Short-Range Goals Prepare report describing the yaw mechanism for a 3T wind turbine. Compare yaw loads of 3T to existing 3R and 2T wind turbines, partly following up on work by Hansen et al. [23] and Saranyasoontorn and Manuel [24]. Provide computer modeling of moments on the yaw bearing and tower. Perform spectral analysis. It was stated in Sec. 6.4 that the rigid hub shows cyclic variability not seen with the teetering hub. This interpretation of graphical data in Fig. 21 should be confirmed with a spectral comparison of the 3R and 3T configurations. Spectral analysis of the existing runs cannot be done because the FAST requirements for linearization were not met. The focus will be the impact of teetering upon the 1P and 3P load cycles of the blade root, yaw bearing, and tower base moments as reported by Lee et al. [15]. Also of interest will be to determine if 3T wind turbines can be spaced more closely in a wind farm than 3R turbines. Compare performance of 3R, 2T, and 3T configurations for offshore analysis. 8.2 Long-Range Goal. The long-range goal is to replace an existing hub on a small commercial wind turbine with the balland-socket hub. Ideally, the size of the wind turbine will enable use of additive manufacturing rather than traditional manufacturing methods. A recent paper by Yim and Rosen [25] provides guidelines for build time and cost estimates using the various additive manufacturing methods. Prior to manufacture, a study will be performed to optimize the design of the ball-and-socket hub. Consideration will be given to providing for adequate space and assembly procedures for pitch motors and transfer assemblies, a means for assembling the hub socket from hub socket housings and hub socket housing connectors, and a means for fitting transfer assemblies within hub sockets. A detailed structural design will then be undertaken to ensure that all components can withstand the loading throughout an extended lifespan of the hub, e.g., 40 yr. It is anticipated that assistance will be needed from a wind turbine manufacturer in order to achieve this goal. Acknowledgment I gratefully acknowledge the support from M. Buhl, B. Jonkman, and J. Jonkman at NREL for their assistance in helping me understand the operation of the various software tools provided by NREL. Nomenclature L ult ¼ ultimate design load for a blade LSS ¼ low-speed shaft (or main shaft) LSSGagMys ¼ bending moment at shaft s strain gage about stationary y s axis LSSGagMzs ¼ bending moment at shaft s strain gage about stationary z s axis LSSTipMya ¼ LSS bending moment about rotating y a axis at the shaft tip LSSTipMza ¼ LSS bending moment about rotating z a axis at the shaft tip Mhn ¼ multi-axial torque about h for blade n RootMxcn ¼ in-plane moment at blade n root about x c (and x a ) axes RootMycn ¼ out-of-plane moment at blade n root about rotating y c (and y a ) axes RootMzcn ¼ pitching moment at blade n root about rotating z c (and z a ) axes Rot_ya ¼ teetering rotation about rotating y a axis Rot_za ¼ teetering rotation about rotating z a axis tdofya ¼ teetering DOF about rotating y a axis tdofza ¼ teetering DOF about rotating z a axis References [1] Ramsland, A., 2014, Horizontal Axis Wind Turbine With Ball-and-Socket Hub, U.S. Patent No. 8,708,654. [2] Ramsland, A., Horizontal Axis Wind Turbine With Ball-and-Socket Hub, U.S. patent application U.S. 13/941,542. [3] Gipe, P., 1995, Wind Energy Comes of Age, Wiley, Hoboken, NJ, p [4] Schorbach, V., Dalhoff, P., and Gust, P., 2014, Taming the Inevitable: Significant Parameters of Teeter End Impacts, J. Phys. Conf. Ser., 524, p Journal of Solar Energy Engineering JUNE 2015, Vol. 137 /