Matching experimental and numerical data of dynamic power train loads by modeling of defects

Transcription

1 WIND ENERGY Wind Energ. (2014) Published online in Wiley Online Library (wileyonlinelibrary.com) PAPER PRESENTED AT AWEA WINDPOWER 2013 Matching experimental and numerical data of dynamic power train loads by modeling of defects Andreas Heege 1 and Jan Hemmelmann 2 1 LMS-SAMTECH, A Siemens Business, C/Paris 205, E Barcelona, Spain 2 GE Global Research, Freisinger Landstr. 50, D Garching b. München, Germany ABSTRACT Defects on wind turbines such as power train misalignments or blade pitch angle deviations are dealt with. These defects cause additional dynamic excitations and thus can reduce the fatigue life of wind turbine components. In order to improve the reliability of dynamic load computations and related fatigue dimensioning of wind turbines, a highly discretized simulation model that incorporates potential system defects is set up. A sensitivity analysis of the impact of system defects on power train dynamics is performed. Experimental measurements of gearbox orbital paths and of the corresponding torque arm loads could be reproduced with good correlation when the simulation model was complemented by power train misalignments and by blade pitch angle deviations. Comparisons of experimental and numerical data are presented in time and frequency domains. Feasible consequences about the impact of alignment defects on the resulting fatigue damage are presented. Copyright 2014 John Wiley & Sons, Ltd. KEYWORDS wind turbine dynamics; high-fidelity simulation model; model validation by experimental measurements; power train misalignment; blade pitch angle deviation; gearbox orbital paths; fatigue loads Correspondence A. Heege, LMS-SAMTECH, A Siemens Business, C/Paris 205, E Barcelona, Spain. andreas.heege@lmsintl.com Received 26 July 2013; Revised 9 December 2013; Accepted 13 December INTRODUCTION In order to evaluate wind turbine power train dynamics and associated loads, an exhaustive experimental measurement campaign was performed on a GE 1.5XLE wind turbine (developed by GE Wind Energy GmbH, Salzbergen/Germany), which was equipped with a GPV 455 gearbox (developed by Bosch Rexroth AG, Witten/Germany). All measurements were performed in the framework of the European UpWind project, a research program that was funded under the EU s Sixth Framework Programme. 1 The experimental measurements revealed a three-dimensional character of wind turbine power train loads and dynamics. In particular, periodic, rotor speed-dependent gearbox orbital paths were identified. In order to reproduce the measured experimental data by numerical simulation, a high-fidelity aerodynamic-mechanical wind turbine model of the GE wind turbine was developed. When the highly discretized aeroelastic wind turbine model was complemented by defects such as power train misalignments and individual blade pitch errors, a good match of experimental data and corresponding numerical results was obtained. The design and sizing of wind turbine power trains require non-linear dynamic load computations 2 4 and fatigue methods that account for all dynamic effects. 5 7 If power trains are subjected to dynamic loading, which induce misalignments, static or linear dynamic analysis methods 8 might miss stress cycles, which are relevant for the dimensioning. It is stipulated that specific combinations of axial, radial and bending loading of power trains can lead to very high stresses at the contact surfaces of bearing and gear components, even if torsional loads are moderate Various topics will be dealt with. First, a brief introduction to computational approaches for dynamic analysis of wind turbines is presented. Next, the setup of the sensors for measurement of dynamic power train loads, deformations and orbital paths is explained. Afterwards, power train transients obtained by coupled aerodynamic-mechanical simulation Copyright 2014 John Wiley & Sons, Ltd.

2 Matching experimental and numerical data of dynamic loads A. Heege and J. Hemmelmann are assessed by comparison with experimental measurements. The comparisons include deformations of the main bearing, torque arm couplings, gearbox orbital paths and load transients of the high-speed shaft (HSS) of the gearbox. Comparisons of experimentally measured and computed transients are performed in time and frequency domains. Consequences for system defects and the resulting impact on the fatigue load spectrum of wind turbine components are presented. 2. COMPUTATIONAL APPROACHES FOR THE DYNAMIC ANALYSIS OF LARGE FLEXIBLE WIND TURBINES In the present study, all numerical simulations have been performed with SAMCEF Wind Turbines, 2 a software package dedicated to the analysis of wind turbine loads and dynamics and that relies on the coupled non-linear finite element and flexible multibody system (MBS) solver SAMCEF-Mecano. 12 The solver SAMCEF-Mecano is based on an augmented Lagrangian formulation and an implicit one-step time integration method of Newmark. 12,13 The incremental form of the equation of motion is stated in equation (1) ½MŠ ½Š 0 Δ q 4 ½Š 0 ½Š 0 Δ λ 5 þ ½CŠ ½0Š " Δ q 4 ½0Š ½0Š Δ λ 5 þ ½KŠ # " # 2 BT Δ q 3 ½BŠ ½Š 0 Δ ¼ 4 R q q ; t 5 λ φð þ 0Δ 2 (1) q; tþ where q is the position vector, q is the acceleration vector, λ is the vector of Lagrange multiplier, [K] is the stiffness matrix, [C] is the damping matrix, [M] is the structural mass matrix½bš ¼ φ = q is the constraint Jacobian matrix, φ is the constraint vector, p is the penalty factor R q q q ; t ¼ g Int: þ F Aero g Ext: ½MŠ q B T λ þp φ is the residual vector Int: g q q q ; t are the internal forces and g Ext: q q q ; t are the external forces. Note that stiffness matrix [K], damping matrix [c], mass-inertia matrix [M], residual vector R q q ; t and constraint Jacobian matrix [B] are non-linearly related to the generalized solution vector f q ; λg. Complementary inertia forces, including centrifugal and gyroscopic effects, are accounted for by internal force vector g Int: q q q ; t.vectorϕ introduces additional equations associated to the Lagrange multipliers λ, which are used to include general MBS functionalities and constraints for controlling the blade pitch angle. The strong coupling of aerodynamics, hydrodynamics and structures is achieved by including in the residual vector R q q q ; t implicitly the equations for aerodynamic and hydrodynamic loads. Details on the time integration procedure, error estimators and solution strategies for equation solvers can be found in the SAMCEF- Mecano user manual Aerodynamic and structural coupling Blades are modeled through a non-linear finite element method (FEM) formalism, which is adapted to large rotations. 2,12 14 For computational efficiency, the structural blade model is presented either in terms of non-linear beam elements or in terms of super elements. Even though super elements are suited to represent complex blade cross sections, the non-linear beam model bears the inherent advantage that material and geometrical non-linearities can be accounted for. In that context, the term geometrical non-linearity refers to deformation/stress-induced non-linearities such as, for example, the blade stiffening under loading/deformation. In contrast to non-linear beam elements, super elements are not suited to represent material or stress/deformation-induced non-linearity. The elemental aerodynamic forces are computed via the blade element momentum theory. The approach includes specific corrections and additional models for the tip and hub losses, turbulent wake state, tower shadow effect, dynamic inflow and dynamic stall (cf. 2,15 21 ). The structural/aerodynamic coupling is performed implicitly at the blade section nodes of the structural blade model through the connection of aerodynamic blade section elements. 2 The latter contributes in terms of elemental aerodynamic forces to the global equilibrium equation. The discretization of the aerodynamic loads corresponds to the FEM discretization of the structural blade model. As depicted in Figure 1, the nodes for the aeroelastic coupling are generally located at the one-fourth chord length positions. There are typically about 15 to 25 blade sections distributed along the blade span. According to equation (2), the relative velocity of a blade section node V rel is formulated implicitly as function of the unperturbed wind speed V Inflow, the blade section speed V BS and the induced velocities V Ind. Taking into account that the aerodynamic loads F I Lift ; FI Drag ; MI Pitch presented in equation (2) are included in the residual vector of equation (1), once the iterative solution of equations (1) is found, the induced velocities, angles of attack, Prandtl loss coefficients and the global structural dynamic response are consistent.

3 A. Heege and J. Hemmelmann Matching experimental and numerical data of dynamic loads Figure 1. Connection of aerodynamic blade section elements. Aero F. q q ; t ¼ F Lift ; F Drag ; M Pitch ¼ 1 2*C i α i q q ; t ρ V 2 rel q q ; t A i with V rel h ¼ V Inflow - V BS þ V Ind i and V Ind h ¼ f ð V Inflow - V BS i (2) Þ; a; a Details on the procedure applied in order to compute the induced speed vector V Ind in terms of the aerodynamic induction factors a and a in the normal and tangential direction, respectively, are given in the references. 2,16,20, Modeling of structural components In order to account for complex dynamic interactions such as, for example, the impact of bedplate vibrations on the HSS deflections and vice versa, structural components and mechanisms are implicitly coupled in one global mechanical model. For the modeling of flexible structural components, a general non-linear FEM formalism that is adapted to arbitrary large rotations 12,13 is applied. For computational efficiency, highly discretized FEM component models are condensed to super elements 22,23 prior to the integration in the global dynamic wind turbine model. Super element condensation is not applied to components that are presented by non-linear beam elements. Non-linear FEM in terms of beam elements are applied to present components such as: Rotor blades Tower model All shafts of the power train including the generator rotor and generator stator Structural components with a geometry that is too complex to be presented by beam elements are discretized using classical FEM modeling in terms of solid or shell elements and then condensed to the kinematic coupling nodes using the super element condensation technique of Craig and Bampton. 22,23 Components that are included in the applied computer model in terms of super elements are: Rotor hub Bedplate including the rear frame Gearbox housing Planet carrier Nacelle structure

4 Matching experimental and numerical data of dynamic loads A. Heege and J. Hemmelmann 2.3. Modeling of mechanisms using an MBS approach Components and mechanisms that are computationally too expensive to be presented by the FEM are included in the global dynamic wind turbine model in terms of an MBS approach. Accordingly, the following mechanisms have been included in the applied wind turbine model in terms of an MBS approach: Pitch and yaw drives including the gaps of the gear systems All bearings of the entire power train including the generator All gear elements of the gearbox Elastic coupling elements for the torque arms Elastic HSS coupling Brake system Elastic couplings of the generator support to the rear frame Electromagnetic generator torque and finally the controller functionalities. The frictional contact problems between flexible gears are reduced to geometrically variable and pointwise flexible contacts. Gear geometry is defined by helix, cone and pressure angles, normal modulus and respective teeth number. Gear teeth flexibility is defined by non-linear gap functions, which account for stiffness variation, when passing along one tooth engagement. Every bearing of the wind turbine, including those of the rotor main shaft, the entire gearbox and the generator, are modeled by non-linear stiffness functions, where bearing clearances are accounted. Even though the mechanical coupling of radial, axial and bending properties can be accounted in the applied methodology, in the present wind turbine model, only the non-linear uncoupled bearing stiffness functions were used. The elastic coupling elements of the gearbox torque arms, the generator shaft coupling and the generator support bushings are modeled in terms of non-linear stiffness functions. The HSS disc brake, which is located in between the gearbox and the generator, is presented by a specific MBS-brake model. The applied brake model accounts for the mechanical coupling of the brake torque and the bending moment, which is generated by the tangential disc brake forces Controller functionalities The controller is implemented in terms of an external dynamic link library for blade pitch, generator torque and yaw control. 2,15 This functionality permits to use the same controller in the numerical model as for the physical wind turbine. 3. SENSOR LOCATIONS FOR POWER TRAIN AND GEARBOX Figure 2 presents the sensor location for the measurements of global power train deformations and orbital paths. Figure 3 depicts the sensors installed within a Bosch Rexroth GPV 455 gearbox (see work of J. Hemmelmann et al. 1 ). 4. DYNAMICS OF MEGAWATT CLASS WIND TURBINES The dynamic properties of megawatt class wind turbines are characterized by some hundred eigenmodes in the low frequency domain up to 50 (Hz). A major part of the elastic deformation energy of an operating wind turbine is contained in dynamic structural deformations modes, which correspond to these eigenfrequencies. These potential resonance frequencies are resulting from the mechanical characteristics of the assembled wind turbine. The global mechanical characteristics are thus resulting from the assembly of the principal components, which include rotor, tower, bedplate, power train and generator components and all the elastic coupling elements to the supporting nacelle structure. The associated deformation energy is generally accumulated simultaneously by blades, tower, supporting structures, the power train and the elastic coupling elements. The number of eigenmodes, which can be presented by the coupled FEM MBS model is equal to the number of degrees of freedom of the computer model. The applied SAMCEF wind turbine model relies on 1332 degrees of freedom. Figure 4 presents two distinct low frequency eigenmodes, which include simultaneously modal-deformations of the blades, the tower and the power train. Local subsystems such as the gearbox require higher spectral resolution in order to capture relevant eigenmodes up to the (khz) domain, which might be excited by the gear mesh frequencies. However, frequencies of below 20 (Hz) include most contribution to the global dynamic deformation energy and cover generally the frequency bandwidth of extreme load

5 A. Heege and J. Hemmelmann Matching experimental and numerical data of dynamic loads Figure 2. Sensor locations for main bearing and power train. Figure 3. Sensor locations within gearbox and measurement point for gearbox orbital paths.

6 Matching experimental and numerical data of dynamic loads A. Heege and J. Hemmelmann Figure 4. Examples of structural eigenmodes, which affect simultaneously several components. transients. In contrast, the frequency bandwidth of load transients, which do not present extreme loads but which are relevant for fatigue, should cover a frequency spectrum up to 1 (khz). It is commented that for the computation of fatigue loads, the applied aeroelastic computer model should cover a sufficient large frequency range and should include all of the relevant eigenmodes, because otherwise, not all fatigue relevant vibration modes will be captured Dynamic excitations of wind turbines Dynamic excitations of wind turbines are composed of contributions, which depend on the rotor speed and on further time-dependent contributions such as, for example, the turbulent wind field. Additional excitations might be induced by the response of the dynamic wind turbine system to the proper controller actions such as blade pitch adaptations. Aerodynamic rotor loads induce unavoidably rotor speed-dependent excitations due to the wind shear, the rotor tilt angle and the effect of the tower shadow. For a three-bladed rotor, these excitation frequencies correspond to three times the rotor speed and are denominated 3P_rotor. In addition to these frequencies and their harmonics, vibrations are identified in experimental measurements of the frequencies 1P_rotor and 2P_rotor, thus corresponding to once or two times the rotor speed. The frequencies of 1P_rotor and 2P_rotor loading might be explained by the presence of drive train misalignments and rotor defects such as blade mass deviations, distinct aerodynamic blade properties or deviations of the blade pitch positions. All these defects result for the drive train in additional bending moments that depend on the rotor speed. Below, some of these characteristic frequencies will be commented for a three-bladed rotor: Frequencies of 1P_rotor and harmonics Frequencies of rotor speed and harmonics are detected systematically in experimental measurements. Fundamental causes for frequency of 1P_rotor and harmonics might be: Individual blade pitch deviations Rotor blade unbalances Misalignment of rotor shaft and gearbox As it will be outlined in Section and depicted in Figure 5, conical vibration modes are characterized by frequencies of 2P_rotor and result from a rotational phase offset of the rotor mass and the mass of the power train with respect to the ideal axis of rotation. Frequencies of 3P_rotor and harmonics Excitation frequencies of three times the rotor speed and its harmonics are induced by the following effects: Wind shear, which induces a vertical speed gradient Rotor tilt angle, which induces additional speed components, which depend on the rotor azimuth position and on the rotor speed

7 A. Heege and J. Hemmelmann Matching experimental and numerical data of dynamic loads Figure 5. Conical rotor modes of frequency 2*P_rotor. Tower shadow effect Elastic blade deformations, which are induced by gravity loads The explicit values of the excitation frequencies for stationary operation at 16.7 (rpm) are summarized in Table I. The excitation frequencies of Table I are depicted by Figures 12, 14 and 16 in terms of the vertical lines in order to facilitate the identification of the corresponding response peaks in frequency domain. Gearbox mesh frequencies Each transmission stage produces speed-dependent excitations, which are due to: Variable gear tooth stiffness Unavoidable misalignments of the power train and gearbox shafts. The aforementioned cited frequencies are systematically detected by experimental measurements. Frequencies produced by controller actionscontroller-actuator frequencies, notch filters and strategies for blade pitch and generator torque influence substantially dynamic loads, as well the excitation of potential resonance frequencies. Turbulent wind fieldthe turbulent wind field presents the main external excitation that has to be controlled through adaptation of generator power, blade pitch and yaw angle position Conical power train vibration modes As depicted in Figure 5, excitations of frequency 2P_rotor might be induced by deformations and misalignments of the rotor relative to the power train masses. An excessive deformation of the rotor shaft and its supporting structure, as well as an important deformation of the elastic gearbox torque arm couplings, might result in a deviation of the rotor rotation axis with respect to the ideal axis of rotation of the power train. The rotor (M1), the gearbox (M2) and generator (M3) might deviate dynamically from the ideal axis of rotation where a phase offset of 180 ( ) of the respective masses can occur. That potential phase offset of 180 ( ) of the respective masses might result in an additional excitation of frequency 2P_rotor. It is assumed that the gearbox orbital paths, which will be analysed in the following sections might be analogous to conical vibration modes, which are observed frequently in classical rotor dynamics. Table I. Rotor speed-dependent excitation frequencies (Hz). Multiples of rotor speed: Associated frequency (Hz): 1*P_rotor: *P_rotor: *P_rotor: 0.84

8 Matching experimental and numerical data of dynamic loads A. Heege and J. Hemmelmann Power train misalignments and individual blade pitch errors In order to improve the match of experimental and numerical gearbox orbital paths, numerous simulation runs were performed with different combinations of defects of the power train alignment and of individual blade pitch errors. Finally, a good match of experimental and numerical gearbox orbitals was obtained when the numerical model was complemented by the following defects. Introduced model defects at the planet carrier coupling Initial angular misalignment at the coupling of rotor shaft and planet carrier: ( ) (lateral Y-axis) ( ) (vertical Z-axis) Initial parallel radial offset in between rotor shaft and planet carrier coupling of: 1.0 (mm) in +Y (lateral direction) 0.1 (mm) in +Z (vertical direction) Introduced model defects at the coupling of HSS and the generator shaft. Initial angular misalignment at the coupling of the HSS and the generator shaft: ( ) (lateral Y-axis) ( ) (vertical Z-axis) Initial parallel radial offset at the coupling of the HSS and the generator shaft: 1.0 (mm) +Y (lateral direction at initial position) 0.1 (mm) +Z (vertical direction at initial position) Introduced model defects at the pitch drives of the rotor blades Pitch drive with blade pitch angle error at one blade of the three-bladed rotor: 1.2 ( ) It is mentioned that all simulations, which included model defects, are based on the aforementioned indicated values of misalignments and blade pitch deviation, except the gearbox orbital, which is presented in Figure 10. Figure 10 is completely analogous to Figure 9, but in that simulation run, the misalignment of the planet carrier coupling was augmented from ( ) to ( ) in order to demonstrate the impact of that potential defect. 5. VALIDATION OF NUMERICAL RESULTS BY COMPARISON WITH MEASUREMENTS The numerical model of the GE-15XLE wind turbine is validated against experimental measurements for two different operational modes. First, experimental measurements and numerical results are compared for energy production under fairly constant wind conditions and, second, an emergency stop maneuver is analysed. The sampling frequency of the experimental measurements is 1 (khz). In the numerical simulations, the time step size is adapted automatically such that the numerical time integration error is kept below a threshold. 12,13 In the presented simulations, the numerical sampling frequency is generally in between 100 (Hz) and 1 (khz) Wind speed measured experimentally with nacelle anemometer Figure 6 resumes the boundary conditions before and respectively after an emergency stop in terms of the wind speed measured by the nacelle anemometer, the wind direction, the generator power, the measured blade pitch angle and the normalized brake pressure of the HSS disc brake, which is located at the exit of the gearbox. It is deduced from the experimental data that measurements are performed under practically constant wind conditions with approximately 9 (m s 1 ) mean wind speed. The considered time interval for the comparisons of energy production extends from time = 100 (s) until time = 150 (s). According to Figure 6, during that time interval, the wind conditions are practically constant; the largest wind direction change is less than 3 ( ) and the maximum wind speed deviation with respect to the mean speed of 9 (m s 1 ) is inferior to 0.7 (m s 1 ). The E-stop maneuver once initiated at time 154 (s) results in a drop of wind speed of about 2 (m s 1 ) as measured by the nacelle anemometer. It is assumed that these variations in the measured wind speed do not correspond to the real unperturbed wind field but are produced by wake effects, which are induced by the sudden blade pitching during the E-stop maneuver.

9 A. Heege and J. Hemmelmann Matching experimental and numerical data of dynamic loads Figure 6. Boundary conditions of examined operation conditions: production operation until time = 154 (s) followed by an emergency stop. The objective was to reproduce wind conditions in the numerical simulation that are similar to the measured wind conditions. So, the same mean wind speed of 9 (m s 1 ) is applied in the numerical simulation as it was measured experimentally. In order to introduce in the wind field of the numerical simulation similar speed deviations as it was measured on the nacelle, the constant mean wind speed is complemented by a speed deviation in rotor direction, which corresponds to 20% of the measured wind speed variation in incoming direction. It is commented that the real standard deviation with respect to mean speed, as well as the spatial turbulence model, cannot be deduced from the wind speed recorded by one sole nacelle anemometer. As a consequence, the spatial variation of the wind field over the rotor plane is simplified, and only a wind shear of coefficient 0.2 is applied to the incoming original wind speed. Other comparisons are performed for an emergency stop simulation. An E-stop simulation is very suited for global model validation. This is because the excitations in terms of blade pitching speed, generator shutdown and brake torque activation are very well defined. Once the blade is pitched sufficiently into the wind, the aerodynamic blade loads are mainly determined by the rotor speed and blade pitch angle. Under these conditions, the impact of a turbulent wind field becomes less pronounced, and the identification of the characteristic frequencies of the wind turbine is facilitated Comparisons for power production in time and frequency domain In the next sections, experimental measurements and numerical results of the gearbox movements for power production are compared under fairly constant wind conditions of approximately 9 (m s 1 ) mean wind speed Gearbox movements and orbital paths for quasi-stationary operation Figures 7 and 8 show experimental measurements and numerical results of gearbox movements in vertical and in lateral directions for two different values of angular misalignments at the planet carrier coupling. The transients which are depicted in Figures 7 and 8 show the movement of the rear of the gearbox housing relative to the bedplate. The corresponding measurement point is located at the rear of the gearbox (see point gear_move B of Figure 2 and of Figure 3). Results of Figure 7 are based on an angular misalignment of ( ), and the results which are presented in Figure 8 are based on a reduced angular misalignment of ( ). All the remaining defects, which are cited in Section are identical for both simulation runs. When the amplitudes of the numerical gearbox movements are compared, in lateral and in vertical directions of Figure 7 as well as of Figure 8, the impact of that alignment defect becomes evident. The gearbox movements, which are presented in Figures 7 and 8 are primarily composed frequencies of 1P_rotor, 2P_rotor and 3P_rotor. Power train vibrations of frequency of 1P_rotor are produced as well by power train misalignments, as well as by an individual blade pitch error, and it is likely that both kinds of defects are a root cause for the experimentally measured frequencies. The numerical model, which was complemented by both defects, namely a blade pitch error of 1.2 ( )

10 Matching experimental and numerical data of dynamic loads A. Heege and J. Hemmelmann Figure 7. Gearbox movement in lateral and in vertical direction with angular misalignment of planet carrier coupling of ( ). Figure 8. Gearbox movement in lateral and in vertical direction with angular misalignment of planet carrier coupling of ( ). and a misalignment of the planet carrier coupling of ( ), reproduced fairly well the measured amplitudes of gearbox movements. Even though all presented transients contain the frequency 3P_rotor, the latter becomes less visible because of the superposition of the defect-induced gearbox movements. In the following, gearbox orbital paths will be compared with experimental measurements. Figures 9 and 10 present the gearbox orbitals for an angular misalignment of the planet carrier coupling of ( ) and respectively of ( ). All the remaining defects, which are cited in Section 4.1.2, are identical for both simulation runs. Orbital paths are presented in terms of two orbits, which are contained in two perpendicular planes. The orbits, which are presented in the upper portion of Figure 9 and of Figure 10 are contained in the plane, which is formed by the longitudinal X-axis (right ordinate) and the lateral Y-axis (abscissae). The orbits which are presented in the lower portion of Figure 9 and of Figure 10 are contained in the plane, which is formed by the vertical Z-axis (left ordinate) and the lateral Y-axis (abscissae).

11 A. Heege and J. Hemmelmann Matching experimental and numerical data of dynamic loads Figure 9. Comparison of measurements and SAMCEF results of gearbox orbital paths with angular misalignment of planet carrier coupling of ( ). Figure 10. Comparison of measurements and SAMCEF results of gearbox orbital paths with angular misalignment of planet carrier coupling of ( ). Numerical data are compared with experimental measurements, on the one hand, for a model without any defect (see light blue plots of Figure 9 and of Figure 10) and, on the other hand, for two different misalignment errors (see blue plots of Figure 9 and of Figure 10). The experimental measurements are presented by the black plots of Figure 9 and of Figure 10. It is deduced from the comparison of the gearbox orbitals that the relation in between an angular defect and the corresponding induced movements is non-linear. According to Figure 9, an angular misalignment of the planet carrier coupling of ( ), produces gearbox movements in lateral and vertical

12 Matching experimental and numerical data of dynamic loads A. Heege and J. Hemmelmann directions, which are generally less than 0.5 (mm). And as Figure 10 shows, twice the angular misalignment produces gearbox movements in lateral and vertical directions, which exceed 1.5 (mm) Deformations of elastic torque arm couplings In this section, the deformations of elastic torque arm couplings are presented in time and in frequency domain for quasi-stationary operation at fairly constant wind conditions with a mean speed of approximately 9 (m s 1 ). The deformations of the left torque arm coupling, which are either obtained by experimental measurements or by numerical simulation, are presented first in time domain. Second, the respective transients are transferred from time domain to frequency domain by means of a fast fourier transformation (FFT). In order to facilitate the identification of rotational speed dependant excitations and/or dynamic responses, the explicit values of the rotor speed dependant excitations for stationary operation at 16.7 (rpm) (Table I) are depicted in the following Figure 11. Axial deformation of torque arm coupling. Figure 12. FFT of axial deformation of torque arm coupling.

13 A. Heege and J. Hemmelmann Matching experimental and numerical data of dynamic loads Figure 13. Lateral deformation of torque arm coupling. Figure 14. FFT of lateral deformation of torque arm coupling. figures in frequency domain by vertical lines. So, Figure 11 presents the axial deformation of the left ( Y) torque arm coupling in time domain, and Figure 12 presents the corresponding FFT of the transients, which are depicted in Figure 11. Analogously, Figure 13 presents the lateral deformation of the left torque arm coupling, and Figure 14 presents the corresponding FFT in frequency domain. Finally, Figure 15 shows the vertical deformation of the left torque arm coupling in time domain, and Figure 16 presents the corresponding FFT of the transient, which is presented in Figure 15. It can be deduced from Figure 12 and from Figure 14 that the dominant frequency for fatigue loading of the torque arm couplings in axial and in lateral directions for quasi-stationary operation corresponds to the frequency of the rotor speed, namely 1*P_rotor. The second highest amplitude corresponds to the frequency of three times the rotor speed (3*P_rotor). A minor peak in amplitudes of the mentioned FFTs is detected systematically for the frequency of twice the rotor speed (2*P_rotor). According to Figure 16, the major contributions to the vertical deformations of the torque arm couplings are of frequencies 1P_rotor and 3P_rotor. In the case of the presented results at the torque arm couplings for quasi-stationary operation, it is concluded that the main fatigue mechanism is related to the additional loads, which are produced by alignment defects.

14 Matching experimental and numerical data of dynamic loads A. Heege and J. Hemmelmann Figure 15. Vertical deformation of torque arm coupling. Figure 16. FFT of vertical deformation of torque arm coupling. The frequency content of the numerical transients and of the experimentally measured torque arm transients show generally good agreement, at least until a frequency of about 5 (Hz) Comparison for emergency stop Figures 17 to 20 present the comparison of experimental measurements and numerical results for an emergency stop. In Figure 17, the rotor shaft torque, the generator speed and the generator power refer to the left ordinate and further plots such as the blade pitch angle, are indicated by the right ordinate. The brake disc torque is only presented by numerical results and refers to the left ordinate of Figure 17. The presented normalized brake pressure transient was measured experimentally and permits to identify the time constants of the brake activation (see dotted red plot of Figure 17). Generator disconnection takes place at the time instance 154 (s), and the activation of the disc brake at the gearbox exit is delayed by 0.01 (s). After activation of the disc brake, braking torque is augmented in 0.1 (s) from zero to full torque of 11 (knm). As shown in Figure 17, blade pitch is constant up to time 154 (s). In the following 10 (s), in order to reverse the rotor torque, the blade is pitched about 90 ( ) in the wind. The wind turbine comes to rest at time 163 (s), and the rotor is oscillating slowly with fixed disc brake. During that phase of very slow rotor oscillations, axial backlashes of the HSS can be identified clearly.

15 A. Heege and J. Hemmelmann Matching experimental and numerical data of dynamic loads Figure 17. Measurements and SAMCEF results for emergency stop (brake pressure is experimental data and brake torque is a numerical result). Figure 18. Measurements and SAMCEF results for emergency stop : axial deformation of main bearing and axial gearbox movement. Simultaneously, Figure 18 presents the axial movement/deformation of the main bearing and the axial gearbox movement. The latter is measured at the elastic torque arm couplings. A comparison of the axial movement/deformation of the main bearing and of the axial deformation of the torque arm couplings reveals that the axial deformations of the torque arm couplings of about 2 (mm) are slightly larger compared with the axial main bearing movement/deformation of about 1 (mm). That phenomenon might be explained by the clearance of the planet carrier bearings, which might permit a relative axial movement in between rotor shaft and gearbox housing of approximately 1 (mm). Figure 19 presents the vertical deformations of the left and of the right torque arm couplings during an E-stop. The right torque arm coupling deforms approximately 0.6 (mm) in traction, whereas the left torque arm coupling is compressed approximately 1 (mm). That unequal deformation of the torque arm couplings might be due to the mechanics of the HSS and disc brake, which are not located symmetrically on the gearbox (Figure 3). As a consequence, especially during braking, an additional bending moment is introduced in the power train and might result in a non-symmetrical deformation of the torque arm couplings. Even though the frequency content of the experimental and numerical transients deviates slightly, the global deformation amplitudes are reproduced fairly well.

16 Matching experimental and numerical data of dynamic loads A. Heege and J. Hemmelmann Figure 19. Vertical deformations of torque arm couplings during E-stop. Figure 20. Bending moment and axial movement of HSS. Figure 20 indicates the axial dynamics and bending loads of the gearbox HSS close to the location of the bearings of the generator side. It is clearly visible how the bending moment on the HSS is increasing when the disc brake at the exit of the gearbox is activated. That increase of the HSS bending moment is due to the frictional forces at the brake pad, which introduce a further bending moment into the HSS. Furthermore, the axial movement of the HSS within the gearbox is displayed in Figure 20. Figure 20 shows the bending moments of the HSS, which are measured close to the generator side bearing and the axial movement of the HSS relative to the gearbox housing (see Figure 3 for the sensor location). It should be noted that the numerical and experimental bending moments show qualitatively the same behavior, but the absolute bending moment values obtained by measurement and respectively numerical simulation deviate substantially. It is mentioned that the sudden augmentation of the bending moment at time = 154 (s) is due to the additional bending moment, which is generated by the tangential brake forces, which are acting at the friction pads of the brake disc. The measured maximum bending moments with values close to 100 (knm) might be either due to a sensor calibration problem or due to dynamic effects, which are not understood. Taking into account that the HSS disc brake moment is about 11 (knm) during the E-stop maneuver, the numerically computed maximum values of the bending moment of approximately 20 (knm) might be due to dynamic amplification and due to additional bending moments, which are generated by the weight of the brake and coupling elements of the HSS.

17 A. Heege and J. Hemmelmann Matching experimental and numerical data of dynamic loads The axial movement of the HSS relative to the gearbox housing is depicted in the same Figure 20. Its values are defined by the right ordinate. Numerical values of the HSS movements and the corresponding measurements show good agreement. 6. CONCLUSIONS The three-dimensional character of power train loads is demonstrated by experimental measurements of dynamic gearbox orbital paths. Measurements indicate that the power train alignment is affected by speed-dependent, periodic deformations that might include conical gearbox orbitals. These gearbox orbitals are clearly visible in measurements and are reproduced numerically with similar amplitude, when alignment defects and individual blade pitch errors are incorporated into the numerical model. It is assumed that conical vibration modes are induced by important rotor shaft bending moments and by the resulting deformations of the flexible couplings of the gearbox suspension. Numerical simulations showed that the relation between the angular misalignment of the power train and the resulting amplitudes of gearbox orbitals is non-linear. Even though good correlation of experimental measurement and numerical results are obtained, further sensitivity analysis is required in order to improve the understanding of the impact of each potential defect on the power train dynamics and associated mechanical stresses. It is concluded that for quasi-stationary operation, the main fatigue mechanism of the torque arm couplings is related to additional load cycles, which are produced by alignment defects. Design rules might be established in order to account already in the design phase for unavoidable misalignments of power train and/or blade pitch deviations. Ideally, specific measurements might validate after commissioning of the wind turbine that static and dynamic misalignments are within tolerances and that the additional load cycles, which result from these defects are accounted for in prior fatigue computations. First, evaluations indicate that these additional excitations result not only in increases of the amplitudes of the gearbox orbitals but cause also a general augmentation of vibrations with a frequency spectrum that is not limited to the excitation frequency spectrum. Further, sensibility analysis is required in order to improve the understanding of the impact of each potential defect on the power train dynamics. Complementary to the comparison of experimental and numerical transients in time domain, analogous comparisons in frequency domain were made. Comparisons in frequency domain of deformation amplitudes showed good correlation between numerical and experimental data up to a frequency of approximately 5 (Hz). For frequencies higher than 5 (Hz), the amplitudes of the numerical results were partially underestimated when compared with the experimental measurements. An underestimation of the amplitudes of the load spectrum in frequency domain is analogous to an underestimation of the corresponding fatigue load cycles in time domain. Analogously, an underestimation of the relevant frequency content of load cycles is equivalent to an underestimation of the number of fatigue cycles in time domain. It is anticipated that the frequency content of insufficiently discretized computer models of multi-megawatt wind turbines rarely exceed some few hertz. In that case, the resulting computational fatigue load spectra will be incomplete because the load cycles of higher frequencies cannot be reproduced by the simulation model. Challenges for improving fatigue predictions exist not only for the reliability of the frequency content of fatigue load spectra. A major challenge is to translate the multidimensional fatigue load spectra of the power train into the corresponding stress spectra of its bearings and gears. For complex dynamic loading conditions, the stresses at the contact surfaces of bearings and gears behave non-linearly and combinations of axial, radial and/or bending loading can lead to high stresses, even if the global power trains loads are moderate. REFERENCES 1. Upwind, 1B2 - Transmission and Conversion. [Online]. Available: (Accessed 15 January 2014). 2. Samcef wind turbines user manual V3.3, [Online]. Available: 3. Peeters J. Simulation of dynamic drive train loads in a wind turbine. PhD Thesis, Katholieke Universiteit Leuven, Belgium, INTEC GmbH. Simpack v8.805 reference manual, Wessling Germany, Sutherland HJ. On the fatigue analysis of wind turbines, SAND , Sandia National Laboratories P.O. Box 5800 Albuquerque, New Mexico Printed June Heege A, Hemmelmann J, Omiciuolo M, Sanchez JL. Comparison of wind turbine component damage computed by linear and fully non-linear fatigue methodologies. EWEC 2010 Proceedings, Warsaw, 2010.

18 Matching experimental and numerical data of dynamic loads A. Heege and J. Hemmelmann 7. Heege A, Adolphs G, Lucas P, Sanchez JL, Bonnet P. Fatigue damage computation of a composite material blade using a "mixed non-linear FEM and super element approach". EWEA 2011 Proceedings, Brussels, March Romax Technology Ltd. RomaxWind simulation software. [Online]. Available: romaxwind.aspx. 9. Whittle M, Shin W, Trevelyan J, Wu J. A parametric study of the effect of generator misalignment on bearing fatigue life in wind turbines. EWEA 2011, Scientific Proceedings of, Brussels, March 2011; Hariharan V, Srinivasan PSS. Vibration analysis of misaligned shaft ball bearing system. Indian Journal of Science and Technology 2009; 2(9): Guo Y, Keller J, Lacava W. Combined effects of gravity, bending moment, bearing clearance, and input torque on wind turbine planetary gear load. AGMA-12FTM EDITION. [Online]. Available: com/standards/show/agma-12ftm Samcef/Mecano. User manual V Samtech SA. [Online]. Available: Geradin M, Cardona A. Flexible Multibody Dynamics: A Finite Element Approach. John Wiley and Sons Ltd.: Chichester, West Sussex PO 191UD, England, Heege A, Betran J, Radovcic Y. Fatigue load computation of wind turbine gearboxes by coupled finite element, multibody-system and aerodynamic analysis. Wind Energy 2007; 10: , John Wiley & Sons Ltd., wiley.com, Bossanyi EA. GH-Bladed User Manual, Issue 14. Garrad Hassan and Partners Limited: Bristol, UK, AeroDyn theory manual, December 2005 NREL/EL Patrick J. Moriarty, National Renewable Energy Laboratory Golden, Colorado A. Craig Hansen Windward Engineering, Salt Lake City, Utah. 17. Jonkman JM, Buhl ML, Jr. FAST user s guide. Technical Report NREL/EL , August Larsen TJ. HAWC2 user manual version 1.4. Risø National Laboratory, April Øye S. FLEX 4 - Simulation of Wind Turbine Dynamics. Proceedings 28th IEA Meeting of Experts State of the Art of Aeroelastic Codes for Wind Turbine Calculations, Technical University of Denmark, Lyngby, Denmark, April 11 12, 1996; Buhl ML, Jr. A New empirical relationship between thrust coefficient and induction factor for the turbulent windmill state. NREL/TP Golden, CO: National Renewable Energy Laboratory, September Snel H, Schepers JG. Joint investigation of dynamic inflow effects and implementation of an engineering method. ECN Report ECN-C , Craig R, Bampton M. Coupling of substructures for dynamic analysis. AIAA Journal 1968; 6(7): SAMCEF-Dynam user manual, version , [Online]. Available: