CUSTOMER APPLICATION | Yihan Xing, Centre for Ships and Ocean Structures (CeSOS), Marine Technology Centre, NTNU

Wind Turbine Drivetrain Modeling In 2002, the Research Council of Norway and the Norwegian University of Science and Technology (NTNU) established the Centre for Ships and Ocean Structures (CeSOS) as a center for excellence. The research at CeSOS aims to develop fundamental knowledge about how ships and other structures behave in the ocean environment using analytical, numerical and experimental studies. CeSOS’ research on offshore wind turbines has focused on modeling dynamic responses of various bottom-fixed and floating wind turbine concepts. Research on the challenges and performance of wind turbine drivetrains used in offshore floating applications has been of particular interest.

three point support (main bearing & two torque arm supports

hub Fig. 1: NREL, Gearbox Reliability Collaborative (GRC)

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main shaft

Yihan Xing, Centre for Ships and Ocean Structures, Marine Technology Centre, NTNU | CUSTOMER APPLICATION

and Analysis Activities at CeSOS

generator

bed plate

generator shaft

gearbox

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CUSTOMER APPLICATION | Yihan Xing, Centre for Ships and Ocean Structures, Marine Technology Centre, NTNU

crucial, as offshore maintenance and repair are costly, and wind turbines are not always accessible due to weather conditions.

Table 1: Model variants

BACKGROUND At CeSOS, researchers use multiple software tools to analyze wind turbines for the sake of comparison. For example, in addition to FAST  [1] and HAWC2  [2], researchers at CeSOS employ software such as SIMO/ RIFLEX [3, 4] for wind turbine global analysis. SIMPACK has been used to model the mechanical components of the drivetrain. This article explores the use of SIMPACK in wind turbine drivetrain research activities within CeSOS. Research on wind turbine drivetrains at CeSOS focuses on the modeling and analy-

USING SIMPACK TO MODEL THE WIND TURBINE DRIVETRAIN CeSOS has utilized SIMPACK to model the wind turbine drivetrain. Load conditions on the drivetrain model are typically calculated using other software codes. For instance, the global analysis of the wind turbine is typically simulated using aero-elastic codes, and the loads at the nacelle are used as inputs for the SIMPACK drivetrain model. SIMPACK has several features that cater specifically to modeling gearboxes. For instance, the Force Element 225 Gear Pair models the gear contact pair using the slicing method, which allows the modeling sis of the drivetrain for offshore applicaof the tooth load distribution along the tions. The wind turbine drivetrain is a crucial tooth flank, also known as the KH� factor. component of the wind turbine. The geared In addition, SIMPACK can model flexible drivetrain concept bodies with complex has been the focus geometries, which are “SIMPACK has several features of CeSOS’s work. The commonplace in wind that are specifically catered to the wind turbine gearbox turbine gearboxes, modeling of gearboxes.” is known as the "misse.g., the planet carrier ing link" in the wind and gearbox housing. industry as it has not achieved its intended Furthermore, the ability to incorporate user routines in SIMPACK allows the modeling of service life of 20 years. It has been blamed for contributing significantly to wind turbine user-defined Force Elements which are very downtime. Understanding the wind turbine useful in research where flexibility in model gearbox for offshore wind applications is definition is important.

Planet A upwind tangential 420

350

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Test M1A M1B M3B P2

300

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360

Force [kN]

Torque [kNm]

250

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Field Dyno 0 20 40 60 Time [sec]

Fig. 2: Test comparison cases 1 (Dynamometer) and 2 (Field)

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100

50

0 50 100 150 200 250 300 350 Carrier rotation [deg]

Fig. 3: Planet upwind loading comparison for test case 1

Yihan Xing, Centre for Ships and Ocean Structures, Marine Technology Centre, NTNU | CUSTOMER APPLICATION

Modeling of rigid planet pins

Modeling of rigid pin interfaces

pin reference node (located in middle of pin)

pin interface reference modes

Modeling of rigid bearings

Modeling of rigid main shaft

of the numerical models used. The in-depth GRC gearbox measurements were used to validate gearbox-modeling techniques and to determine the right compromise between model complexity and accuracy. A set of models that represented different levels of fidelity was constructed. A total of five models were compared; they are presented in Table 1. The main shaft torque time series from the measurements were input directly into the main shaft of the multi-body model. Two test cases were used; these are presented in Fig. 2. The comparison results, presented in Fig. 3, show that the computational models were able to reproduce the planet bearing loads well. This indicates that a multi-body SIMPACK model can accurately reproduce actual test conditions numerically. More details on this work can be found in LaCava et al. [6, 7].

main shaft reference node

bearing reference nodes Fig. 4: Examining the influences of the subcomponents

THE CASE STUDY The gearbox from the Gearbox Reliability Collaborative (GRC) [5] coordinated by the National Renewable Energy Laboratory (NREL), Colorado, USA, was used as the case study for most wind turbine drivetrain modeling and analysis work at CeSOS. The GRC drivetrain is a 750 kW high-speed generator type. It has one planetary and two parallel gear stages and uses the three-point support system. The GRC gearbox within its drivetrain is illustrated in Fig. 1. COMPARISONS AGAINST EXPERIMENTAL MEASUREMENT RESULTS In collaboration with NREL, the experimental measurements from the GRC gearbox were used for extensive model fidelity studies. The GRC has conducted extensive field and dynamometer test campaigns on two heavily instrumented wind turbine gearboxes. The data from the planetary stage is used to evaluate the accuracy and computation time

DETAILED MODELING STUDY OF THE PLANET CARRIER IN THE GRC GEARBOX A detailed modeling study of the planet carrier in the GRC gearbox was also performed. This study was carried out in two parts. First, the influence of the subcomponents mated to the planet carrier in the gearbox assembly was investigated in detail. These components consist of the planet pins, bearings and the main shaft. Fig. 4 shows how these subcomponents were modeled as rigid in order to investigate their influences on the planet carrier. This was performed in Abaqus. Second, the flexible body modeling of the planet carrier for use

proximity sensor at 47° (fixed to DUMMY body) sun gear (output)

planet gear planet gear ring gear

planet carrier (input at the main shaft interface)

Fig. 5: SIMPACK model used for the planet carrier modeling study

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CUSTOMER APPLICATION | Yihan Xing, Centre for Ships and Ocean Structures, Marine Technology Centre, NTNU

3m 3m

4m 48.2 m 54.81 m z x 40 m 70 m

7m line 1

200 m

60°

y

clumped weights line 2

460 m

x

180°

39

.7

600 m

m 610

line 3 300°

m

Fig. 6: The floating spar system for the GRC wind turbine

in SIMPACK is examined through the use of condensed finite element and multi-body models. Both eigenvalue analyses and time domain simulations were performed. Fig. 5 illustrates the SIMPACK model used for this

dummy body (in blue) where the nacelle motions are applied

study. Only the planetary stage was modeled as the focus was on the planet carrier. It was found that the compliance of the planet pins was very important. Using rigid planet pins leads to a very stiff planet car-

r ato ner

ge

loads, motions

Fig. 7: Application of the calculated loads, generator speed and motions as inputs into the drivetrain model. The torque arms and housing casings are not shown.

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ed

spe

rier with many significantly higher eigenfrequencies. Various methods of flexible modeling of the planet carrier were evaluated, and an efficient method of prescribing the Frequency Response Modes (FRMs) was proposed. More details of this work can be found in Xing et al. [8]. MODELING AND ANALYSIS OF THE DRIVETRAIN IN A SPAR-TYPE FLOATING WIND TURBINE In this study, the GRC drivetrain and wind turbine were mounted onto a spar-floating platform to be deployed for offshore wind use. The floating spar system was designed in-house in CeSOS and is similar to the HyWind and OC3 spar concept. Fig. 6 illustrates the dimensions of the design spar platform. This is a catenary moored spar system with three mooring lines. The main purpose of the mooring lines is to keep the structure stationary, with minimal sway. The delta mooring line layout provides additional yaw stiffness. The platform is also ballast-stabilized, which results in large roll and pitch hydrostatic restoring moments due to the low center of gravity. A decoupled solution was used in this instance. First, the global aero-hydro-elasticservo floating wind turbine (FWT) problem is solved using HAWC2  [2]. The loads, generator speed, and motions experienced by the drivetrain in the HAWC2 analysis are then used as inputs for a SIMPACK drive-

Yihan Xing, Centre for Ships and Ocean Structures, Marine Technology Centre, NTNU | CUSTOMER APPLICATION

Main shaft shear forces

Main shaft axial forces

Main shaft bending moments

Main shaft torque

Fig. 8: Comparison of frequency spectra of the axial force, shear force, bending moment and torque on the main shaft. The mean wind speed at hub height is 20 m/s. Radial forces

Tilting moments

PL-B

PLC-B

INP-A

Axial forces

train model. See Fig. 7 for an illustration of the applications of these inputs into the drivetrain model. A comparison of the responses in the FWT and its land-based equivalent counterpart was performed. It was determined that there are general increases in the standard deviations of the main shaft loads and internal drivetrain responses. These increases are larger in the response variables associated with the low-speed planetary stage. This is intuitive as the gearbox has the capability to isolate loads between the individual stages. These differences, however, do propagate to the intermediate- and high-speed stages at the less severe load cases. Comparisons of the frequency spectra (Fig. 8 and Fig. 9) show that wave-induced responses appear both in the main shaft loads and internal drivetrain response variables. More detailed investigations into the individual contributions of the main shaft loads and nacelle motions revealed that the increases in the internal drivetrain responses in the FWT are a result of the increase in the main shaft non-torque loads that the FWT experiences.

Fig. 9: Floating wind turbine vs. land-based wind turbine. Comparisons of the frequency spectra of the INP-A (main bearing), PLC-B (downwind planet carrier bearing) and PL-B (downwind planet gear bearing). The mean wind speed at hub height is 20 m/s.

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CUSTOMER APPLICATION | Yihan Xing, Centre for Ships and Ocean Structures, Marine Technology Centre, NTNU

1600

1st mode

1400

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1200

3rd mode 4th mode

Hz

1000 800 600 400 200 0

600

2.000 kW

5.000

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Fig. 10: Eigenfrequency comparison, 0.6 and 2MW: 3 stages, 5 and 10 MW: 4 stages

DYNAMIC TIME-DOMAIN-BASED TOOTH CONTACT FATIGUE ANALYSIS In this experiment, researchers performed a time-domain-based gear contact fatigue analysis of the GRC gearbox. The main purpose was to investigate how the longterm distribution of gear contact pressures can be represented by analytical functions such as the Weibull distribution and the generalized gamma distribution. These distributions are necessary to design reliable gears using probabilistic approaches and to develop simplified methods for practical design. A new, simplified predictive subsurface pitting model estimates the service lives of gears under dynamic conditions. The decoupled analysis method is used for the dynamic analysis of the gears in the GRC gearbox. First, aero-elastic simulations were performed on the land-based GRC wind turbine using FAST [1]. The main shaft loads calculated from FAST were then used as inputs in a SIMPACK drivetrain model. Three points on the gear teeth were considered for pitting lives as illustrated in Fig. 12. The Weibull and generalized gamma distributions were then used to fit the long-term probabilistic distributions of the gear tooth contact pressures. An example of these fits is presented in Fig. 13.

Frequency (Hz)

The nacelle motions, i.e., inertia forces have excitations are found in the Campbell dialimited contributions to the FWT drivetrain grams. See Fig. 11 for the Campbell diagram responses. of the 10 MW drivetrain. More details of Lastly, an additional main bearing was this work can be found in Nejad et al. [12]. added to the GRC drivetrain to reduce the non-torque loads going into the gearbox. This is Resonance diagram (10.000 KW) the so-called four-point support system. It was found that the 1.000 tooth and bearing loads in the planetary stage are significantly 900 reduced as a result of this additional main bearing. More de800 tails of this work can be found in Xing et al. [9–11]. 700 DYNAMICS OF LARGE OFFSHORE WIND TURBINE 600 DRIVETRAINS In this study, the internal dy500 namics of wind turbine gear trains were examined. The pure torsional model is applied 400 in SIMPACK for eigenmodes analysis and the evaluation 300 of internal excitations by the use of resonance diagrams. 200 The gear trains studied were designed in-house using industrial standards. Case studies 100 of 0.6, 2, 5 and 10 MW were performed. A negative trend of 0 eigenfrequencies was observed 0 5 10 15 20 25 30 in the larger gear trains. This is Rotor speed (rpm) illustrated in Fig. 10. Many possible resonances due to internal Fig. 11: 4-stage drivetrain resonance diagram (10 MW)

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Yihan Xing, Centre for Ships and Ocean Structures, Marine Technology Centre, NTNU | CUSTOMER APPLICATION

4

0

m1

p1: near the point of engagement of the driven gear 0: in the vicinity of the pitch point of the driven gear m1: close to the recess point of the driven gear

2 0

Raw data 2-parameter Weibull generalized gamma 3-parameter Weibull

-2 log (-log(1-Pf))

p1

-4 -6 -8 -10 -12

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-16 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 log (∆Pmax)

4 2

Fig. 12: Positions of the considered points on the gear profile

0

Raw data 2-parameter Weibull generalized gamma 3-parameter Weibull

ACKNOWLEDGEMENTS The author would like to thank William LaCava, University of Massachusetts, Yi Guo, NREL, and Wenbin Dong and Amir Rasekhi Nejad, CeSOS, for their contributions to this article. REFERENCES [1] Jonkman, J., Buhl, M.L., "FAST's User Guide", National Renewable Energy Laboratory, Report number: NREL/EL-500-38230, 2005. [2] Larsen, T.J., Hansen, A.M., "How 2 HAWC2", Risø National Laboratory, Technical University of Denmark, Report number: Risø-R-1597 (ver. 3-1) (EN), 2007. [3] Ormberg, H., Mo, K., "SIMO — User's manual version 3.6", MARINTEK, Report number: 2009. [4] Ormberg, H., Passano, E., "RIFLEX — User's Manual Version 3.6", MARINTEK, Report number: 2009.

-4 -6 -8 -10 -12

Point 0

-14

-16 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 log (∆Pmax)

5

0

log (-log(1-Pf))

CONCLUSIONS The wind turbine drivetrain is a crucial component of the wind turbine that needs to be better studied for offshore applications. Research at CeSOS in drivetrain modeling and analysis uses SIMPACK to accurately model and analyze the wind turbine drivetrain in a variety of research topics.

Complexity using Measurement Validation and Cost Comparison", in: European Wind Energy Association annual event, Copenhagen, 2012. [7] LaCava, W., Xing, Y.H., Marks, C., Guo, Y., Moan, T., "Three-Dimensional Bearing Load Share Behavior in the Planetary Stage of a Wind Turbine Gearbox", under review in IET Renewable Power Generation 2012. [8] Xing, Y.H., Moan, T., "Multi-Body Modelling and Analysis of a Planet Carrier in a Wind Turbine Gearbox", Article accepted in Wind Energy 2012. [9] Xing, Y.H., Karimirad, M., Moan, T., "Effect of Spar-Type Floating Wind Turbine Nacelle Motions on Drivetrain Dynamics", in: European Wind Energy Association annual event, Copenhagen, 2012. [10] Xing, Y.H., Karimirad, M., Moan, T., "Modelling and Analysis of Floating Spar-Type Wind Turbine Drivetrain", Accepted for publication in Wind Energy 2012. [11] Xing, Y.H., Moan, T., Karimirad, M., Etemaddar, M., "Influence of the Design Parameters of a Spar-Type Floating Wind Turbine on Component Loads, with Emphasis on the Drivetrain", Under review in Wind Energy 2012. [12] Nejad, A.R., Xing, Y.H., Moan, T., "Gear Train Internal Dynamics in large Offshore Wind Turbines", in: ASME 11th Biennial Conference on Engineering Systems Design and Analysis, Nantes, France, 2012.

log (-log(1-Pf))

-2

The results indicate that the generalized [5] Link, H., LaCava, W., van Dam, J., McNiff, B., gamma distribution is better than the Sheng, S., Wallen, R., McDade, M., Lambert, S., Weibull distribution, though the twoButterfield, S., Oyague, F., "Gearbox Reliability parameter Weibull Collaborative project “Research at CeSOS in drivetrain is simpler to use. A report: Findings from modeling and analysis uses SIMPACK so-called 'limit-state Phase 1 and Phase 2", to accurately model and analyze function' for contact National Renewable the wind turbine drivetrain...” fatigue analysis Energy Laboratory, could be established Report number: NREL/ based on the pitting life prediction model TP-5000-51885, 2011. presented in this work. More details of this [6] LaCava, W., Xing, Y.H., Guo, Y., Moan, T., work can be found in Dong et al. [13, 14]. "Determining Wind Turbine Gearbox Model

Raw Data 2-parameter Weibull generalized gamma 3-parameter Weibull

-5

-10

-15

Point m1 -20 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 log (∆Pmax)

Fig. 13: Long-term results of the maximum contact pressure range in the sun gear

[13] Dong, W.B., Xing, Y.H., Moan, T., "Time Domain Modelling and Analysis of Dynamic Gear Contact Force in Wind Turbine Gearbox with Respect to Fatigue Assessment", Energies 2012, 5 (11), 4350-4371. [14] Dong, W.B., Xing, Y.H., Moan, T., Gao, Z., "Time Domain based Gear Contact Fatigue Analysis of a Wind Turbine Drive Train under Dynamic Conditions", Accepted for publication in International Journal of Fatigue 2012.

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