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Contract No. DE-AC36-08GO28308

Recommendations on Model 

Fidelity for Wind Turbine 

Gearbox Simulations

Preprint

Y. Guo1, J. Keller1, W. La Cava2, J. Austin3, 

A. R. Nejad4, C. Halse5, L. Bastard6, 

and J. Helsen7

1 National Renewable Energy Laboratory 

2 University of Massachusetts Amherst

3 The Ohio State University

4 Norwegian University of Science & Technology

5 Romax Technology

6 Siemens PLM Software

7 Vrije Universiteit Brussel

To be presented at the Conference for Wind Power Drives (CWD)

Aachen, Germany

March 3‒4, 2015

Conference Paper

NREL/CP-5000-63444

January 2015
NOTICE

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Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 

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Contents

1 Abstract................................................................................................................2

2 Introduction..........................................................................................................2

3 Model Fidelity Study............................................................................................3

3.1 Drivetrain Complexity ....................................................................................3

3.2 Planetary Complexity ....................................................................................4

3.3 Excitation Sources ........................................................................................6

3.4 Imperfections.................................................................................................7

4 Summary ..............................................................................................................7

5 Acknowledgements.............................................................................................8

6 Bibliography.........................................................................................................9
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1 Abstract

This work investigates the minimum level of fidelity required to accurately simulate wind 

turbine gearboxes using state-of-the-art design tools. Excessive model fidelity including

drivetrain complexity, gearbox complexity, excitation sources, and imperfections, significantly increases computational time, but may not provide a commensurate increase in 

the value of the results. Essential design parameters are evaluated, including the planetary load-sharing factor, gear tooth load distribution, and sun orbit motion. Based on the

sensitivity study results, recommendations for the minimum model fidelities are provided.

2 Introduction

Gearboxes in wind turbines do not always achieve their expected design life [SS13]; 

however, they commonly meet or exceed design criteria as specified in current standards by the gear, bearing, and wind turbine industries and by third-party certifications. 

The National Renewable Energy Laboratory’s Gearbox Reliability Collaborative (GRC) 

was established by the U.S. Department of Energy in 2006. Its key goal is to understand the root causes of premature failures and improve reliability using a combined 

testing-and-modeling approach.

Modeling the planetary section of wind turbine gearboxes can be quite complex, and 

excessive fidelity can significantly increase computational modeling time to the point 

that it becomes detrimental to obtaining an understanding of the planetary behavior. 

The challenge, then, is to determine the level of complexity required to accurately 

simulate planetary load sharing and motions. Facets of model fidelity include: 

• Drivetrain complexity: For example, is modeling the main shaft or main 

bearing(s) needed? Is modeling the intermediate and high-speed stages 

needed? Is modeling the gearbox trunnion mounts or generator coupling 

needed? Can the planetary section be decoupled from the rest of the system?

• Planetary system complexity: When modeling the planetary section, how many 

degrees of freedom, number of elements, or modes are needed? Is flexibility of 

the ring gear or housing needed? Is detailed gear and bearing microgeometry 

needed?

• Excitations: Are gravity, dynamic loads, or gear and bearing stiffness variations 

needed?

• Imperfections: Are shaft misalignment, bearing clearance, gear tooth position 

errors, runout, and eccentricity important? These quantities vary from one

gearbox to another and over time. If they significantly affect the planetary loadsharing characteristics, then a probabilistic approach to gearbox modeling is 

required.
3 

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The objective of this report is to examine the effects of model fidelity on measured 

planetary loads and motions. Modeling results from multiple tools that have varying 

levels of complexity are compared to each other and to GRC experimental data. 

3 Model Fidelity Study

Multiple gearbox modeling tools and a simple lumped-parameter model were used to 

simulate the GRC gearbox dynamics in this study. Additional details about each model 

are discussed in a lengthier paper [YG15]. 

Various decisions about model complexity, excitations, and imperfections were made 

while modeling the GRC drivetrain to accurately capture the gearbox response. During 

the decision-making process, extensive sensitivity studies were conducted to 

understand the individual and combined influences of model parameters on the 

aforementioned design parameters. These studies helped establish the appropriate 

model fidelity, boundaries, and excitation features.

3.1 Drivetrain Complexity

Studying drivetrain complexity can determine the appropriate model boundaries, such 

as whether the gearbox should be modeled alone or modeled with the connection to the 

upwind main shaft/bearing and downwind generator/generator coupling.

Image 1 shows the planet gear upwind bearing load calculated using the model with the 

gearbox alone and the model with the gearbox and main shaft/bearing together

compared to the experimental results. Without the main shaft and bearing, the planetbearing loads were nearly constant. With the main shaft and bearing, the calculated 

bearing load fluctuated and the amplitude better matched the experimental results. 

Image 1. Effect of main shaft/bearing modeling on upwind planet-bearing force
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The bearing load fluctuations are caused by the rotor nontorque loads [YG141]. 

Including the main bearing/shaft is important to capture the nontorque load path to the 

gearbox. Further, the weight of the main shaft itself is an additional source of nontorque 

load that can affect the gearbox’s internal response.

The gearbox trunnions support the gearbox weight and limit its torsional windup. At the 

same time, the trunnions allow axial and tilting motions of the gearbox. These trunnions 

are important elements to take into account in the model. The effect of generator shaft 

misalignment is being examined in current dynamometer testing.

3.2 Planetary Complexity

The study of planetary complexity focuses on gear tooth modifications (some simple 

gearbox models do not consider gear tooth modifications), ring gear flexibility, bearing 

clearance, and the spline connection. Image 2 compares the modeling results of the 

sun orbit amplitude calculated using the model with and without modifications and 

measured through experiments. The amplitude of the model without tooth modifications 

is more than double that with tooth modifications. The modeling results with tooth 

modifications are closest to the experimental results. The lack of modeling gear profile 

and lead tooth modifications leads to unexpected gear vibrations caused by an

overestimated transmission error.

To model profile and lead modifications, gear tooth flanks in multibody dynamic models 

are typically divided into multiple slices. A convergence study was conducted to 

determine the optimal number of gear tooth slices. The optimum number of slices was 

determined to be 35, as shown in Image 3; however, using a large number of gear 

slices significantly increases the computational time.

Image 2. Effect of the tooth microgeometry on sun 

gear motion amplitude

Image 3. Effect of the number of tooth slices 

on gear tooth load [WL12]
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Accurate peak and mean loads are needed for a gear designer to measure the gear 

design parameter tooth load distribution factor, khβ. Image 4 shows the calculated and 

measured khβ on the ring gear teeth at 0-, 120-, and 240-degree circumferential 

locations around the ring gear. The model includes 35 flank slices per gear. The model 

and the experimental data agreed reasonably well. Using a single tooth slice per gear

(such as in a two-dimensional lumped-parameter model) leads to a line shape of khβ 

instead of the actual parabolic shape, as shown in Image 4. Therefore, it is important to 

include tooth microgeometry modifications to obtain accurate gear motion (Image 2) 

and tooth load distributions (Image 4). Futher, an accurate khβ is needed to calculate 

the planet-bearing load distribution among the upwind and downwind rows.

Image 4. Ring gear tooth load distributations at (left) 0-, (middle) 120-, and (right) 240-degree

circumferential locations

Internal bearing clearance and preload are crucial modeling parameters that affect 

bearing load zone and stiffnesses. The effect of carrier-bearing clearance on planetary 

gear loads at several torque levels is shown in Image 5. Modeling results using 

analytical and computational approaches compared well to available experimental data. 

The carrier-bearing clearance was nondimensionalized by dividing it by the motion 

amplitude of the carrier when the carrier bearing had infinite clearance. The operating

carrier-bearing clearance was 275 μm, and the planet-bearing clearance was not 

considered. Planet bearings were not in the nontorque transfer path to the gear teeth; 

therefore, the effects of planet-bearing clearance on load sharing were significantly less 

than those of carrier-bearing clearance. Increasing the carrier-bearing clearance clearly 

increased the load-sharing factor. When the carrier-bearing clearance became larger 

than the carrier motion with infinite clearance, the load-sharing factor converged to a 

constant. Additionally, the lower the torque, the more carrier-bearing clearance 
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increased the load-sharing factor. At low torque, the load-sharing factor was high,

because the nominal planet gear loads decreased with torque.

Image 5.Effect of carrier-bearing clearance on load-sharing factor [YG12]

3.3 Excitation Sources

Gearbox internal excitations are from the time-varying gear-meshing action and the 

stiffness variations of rolling-element bearings [YG142]. External excitations are 

primarily nontorque loads transmitted from the turbine rotor and gravity forces.

Planetary load sharing is affected by bearing clearance, as described above, but even 

more so by nontorque loads (including gravity), as described in this section.

Image 6. Load-sharing factor sensitivity [YG12] Image 7: Simulated sun motion caused by various 

manufacturing errors [JA13]

0 50 100 150 200 250 300 350

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

Carrier Rotation, Deg

Sun X-motion, mm

No Error

75um Pin Error & Planet Runout

75um Pin Error

150um Pin Error
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Image 6 shows the computational results of the planetary gear load sharing with 

various values of main shaft pitching moments. The carrier-bearing operating clearance 

was 275 μm, and the planet-bearing clearance was 0. The rotor-bending moment 

increased the load-sharing factor fairly gradually, until it was equivalent to the input 

torque. Beyond that, a large bending moment induced nonlinear tooth contact and 

sharply increased the load-sharing factor, particularly for the 10% torque condition. In 

that case, the gear tooth load contact pattern changed from a slightly disturbed load 

distribution when the nondimensional bending moment was less than 0.02, to edge 

loading when larger than 0.02, and eventually reversing contact when larger than 2.

3.4 Imperfections

This study investigated planet pin position error, planet pin looseness, and planet 

runout. The first two imperfections were measured on the GRC gearbox [AN14]. The 

sun gear orbiting motion is a combined effect of planetary load sharing, sun spline 

stiffness, and manufacturing and assembly tolerances. Among all tolerances, the errors 

that disturb the planet symmetry have a greater influence on sun motion—for example, 

the planet pin position error, planet runout, and carrier eccentricity. As shown in Image 

7, the sun motion for the nominal case without errors had little variation.

Increasing pin position errors induced sun motion at a once-per-carrier revolution with 

increasing amplitude. There is a linear relationship between pin position error and sun 

motion. Planet runout adds an additional sun motion component at the frequency of 

planet rotation. This is superimposed on the motion because of the pin position error.

Compared to Image 2, the motion variation without pin errors shown in Image 7 is much 

smaller, because the modeling tool used to calculate it solved for only the static 

response of the system and ignored the dynamics.

4 Summary

The recommended modeling approaches for major gearbox and drivetrain components

are given in Table 1. Table 2 lists other important modeling elements, including gearbox 

internal nonlinearities, excitation sources, and manufacturing errors. These recommendations are based on the GRC gearbox and three-point drivetrain configuration, which 

is representative of a majority of drivetrains. Detailed results that support these recommendations will be included in a separate publication in 2015.
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Component Recommended Approach Degree of Freedom Requirements

Rotor/hub Rigid body with lumped weight N/A

Main shaft Flexible, FE beams Determined by convergence study

Main bearing Stiffness matrices 5 (exclude rotation)

Gearbox housing Flexible, condensed FE Determined by convergence study

Planetary carrier Flexible, condensed FE Determined by convergence study

Gearbox shafts Rigid shaft N/A

Gearbox support Stiffness matrices 6

Gears Rigid body with contact stiffness 6

Gearbox bearings Stiffness matrices 5 (exclude rotation)

Spline Stiffness matrices 2 (tilting)

Bedplate Rigid body or condensed FE N/A

Generator coupling Stiffness matrices 5 (exclude rotation)

Table 1. Minimum model fidelity for the study of gearbox internal motion

Other parameters Effects Priority

Manufacturing 

tolerance

Affects component motions but has limited effects on 

loads

Medium

Bearing clearance or 

preload

Affects component motion and loads. Operational 

values with operating temperature are recommended.

High

Gear tooth microgeometryAffects frequency spectrum of component motions and 

gear tooth and bearing load distributions

High

Bedplate tilting angle Causes gearbox axial loads because of gravity Medium

Gravity Affects component motion and loads High

Nontorque loads Affects component motion and loads High

Gear mesh stiffness or 

transmission error

Affects frequency spectrum of component motions Medium

Table 2. Other important modeling parameters that affect gearbox motion

5 Acknowledgements

This work was supported by the U.S. Department of Energy under contract number DEAC36-08GO28308 with the National Renewable Energy Laboratory.
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6 Bibliography

[SS13] Shuangwen Sheng:

Report on Wind Turbine Subsystem Reliability

In: NREL/PR-5000-59111, Golden, CO

National Renewable Energy Laboratory, 2013

[YG15] Yi Guo et al:

Gearbox Reliability Collaborative Modeling System Practice

In: NREL/TP-5000-60641, Golden, CO

National Renewable Energy Laboratory, 2015

[YG141] Guo, Y.; Keller, J.; Parker, R. G. 

Nonlinear Dynamics and Stability of Wind Turbine Planetary Gear 

Sets under Gravity Effects.

In: European Journal of Mechanics A/Solids, vol.47, 2014.

[WL12] LaCava, W.; Xing, Y.; Guo, Y.; Moan, T. 

Determining Wind Turbine Gearbox Model Complexity Using 

Measurement Validation and Cost Comparison.

In: EWEA Proceedings, Copenhagen, 2012.

[YG142] Guo, Y., Eritenel, T., Ericson, T., and Parker, R. G.

Vibro-Acoustic Propagation of Gear Dynamics in a Gear-BearingHousing System.

In: Journal of Sound and Vibration, vol.333(27), 2014.

[YG12] Yi Guo et al:

Combined Effects of Input Torque, Non-Torque Load, Gravity, and 

Bearing Clearance on Planetary Gear Load Share

In: NREL/TP-5000-55968, Golden, CO

National Renewable Energy Laboratory, 2012

[AN14] Nejad A.R., Xing Y., Gao Z., Moan T.

Effect of floating sun gear in wind turbine planetary gearbox with 

geometrical imperfections.

In: Wind Energy, DOI:10.1002/WE.1808, 2014.

[JA13] Jason Austin:

A Multi-Component Analysis of a Wind Turbine Gearbox using A 

High Fidelity Finite Element Model

In: Masters Thesis, Columbus, OH

Ohio State University, 2013