Sources of time-varying contact stress and misalignments in wind turbine planetary sets



Recent data shows that 90% of large wind turbines include a gearbox, and industry forecasts expect this figure to remain relatively stable. With global annual volumes (2009) of around 18,600 units, the quality, cost and performance of gearboxes is of paramount importance to the wind sector. The industry has been focusing some attention on gearbox reliability, as demonstrated by a growth in the number of specific seminars and collaborative programs on this topic. One aspect that needs to be brought to an industry-wide forum is the understanding of the complexity of bearing design in the gearbox and the careful attention that needs to be paid to ensure a reliable gearbox design. This paper seeks to address this issue by clear demonstration of design issues using a model of the gearbox from the National Renewable Energy Lab's Gearbox Reliability Collaborative. Detailed models are presented with focus on determining the quality of the function of the planetary gear stages. Key design drivers are discussed such as the quality of alignment at the gears and bearings and the loads and stresses seen on these components. Under a design load case with a significant rotor off-axis moment the stresses in the planet gears and bearings are investigated. It is shown how the misalignment of the planet pins varies with the rotation of the planetary set and how subsequently time-varying contact stresses and load distributions occur in the planet gears and bearings. These factors strongly influence the fatigue life of the gearbox components as well as the level of vibration. Design tools are then used to demonstrate how small variations in the clearances of the planet carrier bearings can have a big effect on the quality of the design. Numerical studies show where optimal clearance settings lie and how the misalignment of the planetary set can be improved. Furthermore, a demonstration is made of how redesign of the bearing arrangement and subsequent optimization of the planet tooth geometry further improves the misalignment and results in significantly reduced time-varying contact stresses, better load distribution and reduced vibration. It is illustrated that small clearances, such as in the carrier bearings, can have a large effect on the performance of the design and a study shows how to identify and reduce time-varying misalignment and contact stresses resulting in lower vibration, lower fatigue and a more reliable product. Copyright © 2011 John Wiley & Sons, Ltd.


The wind industry grew in the first decade of the 21st century at rates consistently above 20% a year in terms of global cumulative installed capacity (MW) (see Figure 1). The offshore wind is booming with the market, growing 54% in 2009 with 199 new turbines (577  MW). There are 17 new offshore farms being constructed, totaling over 3500  MW, and 52 farms that have been approved representing over 16,000  MW.2 There is political and public pressure behind the wind industry to boost this renewable energy sector with ambitious plans; such as 20% wind energy by 2030 in the USA3 and the continuously increasing 2020 targets in China.4

Figure 1.

Global installed capacity from 2000 to 2009.1

Accompanying the growth in demand and installed capacity is the growth in the size of the machinery. In 2001, the global average size of installed turbines was 0.93  MW, and by 2008, this metric had reached 1.53  MW.5 The biggest turbines are intended for the offshore market, for example, 48 Repower 6  M (6  MW) turbines are being built at the Nordsee Ost Wind Farm with a planned commissioning in 2012.6

Alongside this rapidly expanding market and growing machinery is a significant issue with the reliability of rotating machinery, and there is an industry focus is on improving gearbox and bearing life. In Tayner et al.,7 reliability statistics are given for European databases of wind turbine failures, and the analysis of the Landwirtschaftskammer (LWK) survey of up to 643 wind turbines is reproduced here in Figures 2 and 3. The statistics show that the drive train (gearbox and main shaft) has significant failure rates, and also a gearbox failure yields the highest downtime. It is also one of the most expensive components to replace; a 2  MW wind turbine gearbox may cost between 200,000 and 400,000 depending on type and manufacturer, of which 50,000–100,000 may be required just for the bearings, the latter more appropriate where the turbine main bearing is integrated into the gearbox (e.g. a large double row taper roller bearing). With gearbox failure come additional costs for removal and replacement and for loss of energy capture.

Figure 2.

Failure rate of wind turbine components.7

Figure 3.

Hours lost per failure for wind turbine components.7

The growing market and need for improved reliability and robust designs have brought an industry-wide effort, such as the development of a new IEC standard 61400-4, Wind Turbines—Part 4: Design and Specification of Gearboxes (replacing ISO 81400-4:2005) and the National Renewable Energy Laboratory Gearbox Reliability Collaborative (NREL GRC),8 a large multi-year project that brings together a range of participants across the industry for analysis and testing of wind turbine gearboxes. This paper presents several topics stemming from participation in the NREL GRC that address issues in design, reliability and behavior of the rotating machinery in wind turbines. The paper details some aspects of the state of the art in simulation technology and design approaches used in the industry.


The GRC is a program run by the NREL National Wind Technology Centre to determine the reasons for premature failure that are common in gearboxes in wind turbines. The GRC focuses on three areas of research: drive train modeling and analysis, full-scale dynamometer testing and field testing. Figure 4 shows a solid model of the GRC gearbox as it would be installed in the wind turbine nacelle and Figure 5 the corresponding system (excluding the hub) under test at the NREL dynamometer test facility in Golden, Colorado.

Figure 4.

Solid model of GRC gearbox installed on wind turbine bedplate.8

Figure 5.

Romax Technology engineer on site at NREL working on the GRC gearbox (installed on bedplate in dynamometer test facility).

Two 750  kW gearboxes have had some redesign from the original arrangement and been modified to allow a comprehensive instrumentation package (over 150 channels) that provides measurements of tooth root strains on the ring gear, raceway strains on the planet bearings, deflection of the planet carrier, temperatures near the bearings, input and output torque and speed and more.

Romax Technology is involved in the program and the following sections discuss the application of various simulation technologies and findings related to the program. For more details on the GRC, see Oyague et al.8


The gearbox has been modeled in the RomaxWind software,9 (Romax Technology Ltd, Nottingham, Nottinghamshire, UK) a virtual product development and simulation environment for the design and analysis of wind turbine gearboxes, bearings and drive trains. A model of the GRC gearbox is shown in Figure 6, with some salient features labeled. The gearbox is a single-stage planetary with two parallel helical gear stages—a typical configuration for medium-sized gearboxes in wind turbines. The gearbox is a speed increaser, with approximately 1:81 ratio and is designed for high-speed shaft speeds of 1200 and 1800  rpm depending on the running configuration of the two speed (4/6 pole) generator.

Figure 6.

RomaxWind model of GRC gearbox.

Some key features of the model include beam finite element representation of shafts, solid finite element representation of gearbox housing, gear blanks, planet carrier and torque arms and 6 degree-of-freedom spring connections for (elastomeric) trunnion mounts. The gears and bearings are modeled with semi-analytical formulations that take account of important factors such as misalignment, area of contact under load, microgeometry, radial and axial clearances or preload and material properties. Static nonlinear analysis can be performed for prescribed loading conditions and the global deflections are solved simultaneously with the contact mechanics for the gears and bearings. Static analysis is considered sufficient as the inertia terms are orders of magnitude lower than the forces because of the loads carried by the gearbox. Thus the effect of the whole system behavior on contact elements is captured. Designers use these models for achieving good alignment of the system under the loads, calculating gear and bearing contact stress and life, optimizing the microgeometry of the gears for increased life and transmission error and predicting the gear vibration magnitudes, as well as for many other purposes.

The gearbox model is used in this paper in various forms to illustrate technology and design approaches important to improving wind turbine gearbox reliability, and Figure 7 provides one arrangement where the gearbox is modeled as installed in the NREL dynamometer test cell (Figure 8)

Figure 7.

RomaxWind Model of GRC gearbox.

Figure 8.

GRC gearbox on bedplate (top left in image) in NREL dynamometer test (the dynamometer gearbox is in the foreground).


Figure 9 provides a model for the purpose of simulating the GRC gearbox as installed in the wind turbine. The load case shown with the figure includes a significant off-axis moment as well as loading from rotor mass (wind turbine blades and hub). Large off-axis moments are common in wind turbines, under conditions such as wind direction change, yaw error (putting the blades askew to the wind), yawing of the machine and wind shear. Most dynamometer tests only load the drive train with torque, and it is important to understand that the loading and deflections of the gearbox may be markedly different in the two installations; particularly for three-point mounting arrangement (main bearing and two torque arm supports).

Figure 9.

RomaxWind model of GRC gearbox installed in wind turbine with load case.

For the given load case, a nonlinear static analysis has been performed and the contact and stress in the planetary stage is calculated at a certain carrier rotation. Planet positions are shown in Figure 10, and subsequent results focus on the planet/sun gear mesh and the planet and carrier bearings indicated in the figure.

Figure 10.

RomaxWind model showing planet positions at nominal carrier rotation.

Examining the three-point mounting arrangement, it is clear that moments about the main bearing must be supported by the gearbox mounts and the load path is then through the carrier bearings and housing. The load as well as clearance in these bearings can misalign the carrier to the housing and ring gear and affect the gear contact. (Note that the main bearing is a spherical roller and provides little tilt stiffness). Figure 11 provides the contact distributions at the sun/planet mesh, and maximum contact stress, gear misalignment and face load distribution (Table I) are three metrics generated from these results to judge design quality and are used in fatigue life calculations.10 For planet positions 1 and 2, the contact distribution for the gears is poor (edge loaded) because of misalignment under the load condition. Large loads traversing the edge of the face width will lead to high edge stresses in the gear teeth and result in premature tooth failure.

Figure 11.

Sun/planet load distribution at (a) planet position 1, (b) planet position 2 and (c) planet position 3.

Table I. Metrics on the quality of gear contact for planet positions shown in Figure 11.
Planet positionMaximum contact stress (MPa)Misalignment FβX (µm)Face load distribution factor K
31197 57.21.35

The contact stresses for the downwind planet bearings are shown in Figure 12; the corresponding values for maximum stress is provided in Table II. As seen with the sun/planet load distributions, there is greater edge loading on the planet bearings, which is undesirable from a reliability stand point of view. Seven rollers share the load in each position. The varied contact stresses indicate that there is a significantly varying contact stress in both the gears and bearings of the planetary stage.

Figure 12.

Load distribution at the downwind planet bearings for planet positions shown in Figure 10; greater edge loading is pointed out at 240°C.

Table II. Metrics on the quality of bearing contact stress for planet positions shown in Figure 11.
Bearing position (°C)Maximum contact stress (MPa)

4.1. Time-varying misalignment and stress

When the planet carrier rotates, the planets 1, 2 and 3 move with the carrier, and subsequently, the planet load share and planetary gear misalignment vary with time. This results in increased vibration and reduced life, increasing the probability of failure for the planetary gear set. By performing the analysis at incremental rotations of the carrier, the time-varying behavior can be examined, and Figures 13 and 14 chart the planet load share and sun/planet gear misalignment, respectively. The time-varying alignment and load sharing have significant effects on the planet bearings, a component that is problematic in wind turbines and expensive to replace. In the design process, the loaded contract distributions at the bearings are calculated and assessed for good alignment and acceptable stress, and then calculations across the whole design load spectra are used to predict fatigue life.10

Figure 13.

Planet load sharing with carrier rotation.

Figure 14.

Sun/planet gear misalignment with carrier rotation.

Figures 15 and 16 show an example roller stress distribution for planet 3 at 150°C and 320°C rotation, and these plots represent at a point in time where an arbitrary roller is centered at the point of maximum stress in the load zone. At the 320°C planet position, the stress is highest and the load distribution skewed to one edge.

Figure 15.

Downwind planet bearing maximum contact stress with carrier rotation.

Figure 16.

Roller stress distribution on planet 3 downwind bearing at 150°C carrier rotation.

The carrier bearing stress varies with the carrier rotation as well, but the amplitude of variation is small. The carrier bearings have acceptable levels of contact stresses as shown in Figure 17.

Figure 17.

Roller stress distribution on planet 3 downwind bearing at 320°C carrier rotation.

4.2. Optimizing the design to improve contact, stress and life

A design analysis needs to be performed to understand the influences on the misalignment on the planet gears. If the misalignment can be reduced, then the time-varying contact stress and face load distribution can be reduced. This will in turn decrease vibration and reduce fatigue on the planet gears and planet bearings.

For many wind turbine gearbox designs, the alignment of the planetary stage is sensitive to the magnitude of the clearances in the planet carrier bearings (i.e. the bearings that support the carrier). For this model (Figure 9), with the gearbox installed in the turbine, a full factorial study has been performed where the radial internal clearance of the upwind and downwind planet carrier bearings are varied, and the misalignment and face load distribution factor (FβX and K11) are calculated for each planet position of Figure 10. Note, for the results of Figures 11, 15–17, the clearance was assigned as 260  µm for both carrier bearings. The factorial study (Figure 17) demonstrates how sensitive the misalignment of the sun and planet is to these bearing settings, and designers can use such models to optimize the settings of the bearings.

The best clearance specification would be the subject of a full design review; however, a brief example is provided here where the carrier clearances are set to an optimal value so that the planet/sun misalignments are consistent with position. For this design and load case, these optimum settings are 50/250  µm on the upwind/downwind bearings (indicated by markers on Figure 18, compare Figures 19 and 20 for the downwind planet bearing maximum contact stress). With the optimized clearances, a similar mean stress is achieved; the maximum stress is reduced by approximately 5% and the time-varying amplitude is reduced by a factor of 4. The gears are still misaligned, yet this misalignment is now consistent with rotation (plot not shown) and can be corrected with lead slope adjustments.

Figure 18.

Downwind and upwind carrier bearing maximum contact stress variation with carrier rotation.

Figure 19.

Results of full factorial study for upwind and downwind planet bearing clearance: (left) sun/planet misalignment FβX; (right) sun/planet load distribution, K.

Figure 20.

Downwind planet bearing maximum contact stress with carrier rotation after planet bearing clearance optimization.


5.1. Effect of optimization

The improved carrier bearing clearance setting leads to lower vibrations levels in the components of the gearbox. This in turn leads to better life and improved reliability as the load distribution and load sharing in the planetary stage are improved. But can we really rely on such tight bearing settings on the carrier roller bearings? Typical manufacturing tolerances on bore of the carrier and planetary alignments are of the order of 100 microns. This would mean that even though we can specify clearances while designing the gearbox, in practice, we may not achieve the most optimum settings. A change of a few microns affects the load sharing significantly. This prompts the use of other design decisions to reduce the sensitivity of the model to bearing clearances.

The types of design decision typically investigated in such a scenario may include:

  • two-point mounting versus traditional mounting methods,

  • two-point mounting with torque only mount,

  • Adding more planets,

  • Using flexible pins in the design,

  • Changing the bearing package.

Some of these would not be feasible based on the gearbox under study. In the following section, a case study of changing the bearing package is presented.

5.2. Change of bearing package

In the following case study, we have replaced the cylindrical roller bearing of the carrier with tapered roller bearings. A full factorial study was then performed to analyse the effects of preload on misalignment (FβX) and face load distribution factor (K) (see Figure 21).

Figure 21.

Results of full factorial study (−200 to +200 microns) for carrier bearing preload: (left) sun/planet misalignment FβX; (right) sun/planet load distribution, K.

For an operating setting with a 100 micron preload, lower variation of planet gear misalignment and load distribution with carrier rotation was observed. The load distribution on the planet bearings was also more uniform (no edge loading) as can be seen in Figure 22 and from the tabulated values in Table III.

Figure 22.

Load distribution at the downwind (left) and upwind (right) planet bearings for 0°C carrier rotation for planet 1 (from position in Figure 10).

Table III. Metrics on the quality of bearing contact stress for 0°C carrier rotation for planet 1.
BearingMaximum contact stress (MPa)No. of roller in contactLoad Zone Factor

5.3. New bearing package with microgeometry optimization

Microgeometry correction on the planet gear set can be made to correct gear misalignments and improve the face load distribution. Figure 23 shows the improvement in the gear contact at the face of the planet gear 1 (which had extreme loading pattern in the original case) with a changed bearing package and changes in the lead slope. The corresponding metrics on the quality of contact are shown in Table IV. Similar improvements are noticed for the contact patches on planet gears at positions 2 and 3. Thus, an overall reduction in planet gear misalignments and a corresponding improvement in face loading can be obtained through the use of advanced design tools such as RomaxWind to make design assessments.

Figure 23.

Sun/planet load distribution for (a) original case with CRB, (b) TRB with +100  µm preload and (c) after microgeometry optimization.

Table IV. Metrics on the quality of gear contact for cases shown in Figure 23.
CaseMaximum load per unit length (N/mm)Face load distribution factor K
(b) 9491.39
(c) 9211.11

The improved design is quite robust, and small errors in planet position because of assembly don't affect the load sharing patterns.


Improving the reliability of wind turbines is important for the industry and for reducing the cost of energy. The NREL GRC program is one example of the industry working together to improve the understanding of the gearbox and exploring and disseminating the reasons for premature failure. This paper has reviewed aspects of the program and provided some of the contributions of one industry participant. Detailed models within the RomaxWind software tool have been developed with focus on determining the quality of the function of the planetary gear stages, and predictions of planet load distributions have been validated against the test data. Key design drivers are discussed, such as the quality of alignment at the gears and bearings and the loads and stresses seen on these components. It is illustrated that small clearances, such as in the carrier bearings, can have a large effect on the performance of the design and a study shows how to identify and reduce time-varying misalignment and contact stresses that leads to lower vibration, lower fatigue and a more reliable product.


The authors would like to acknowledge the National Renewable Energy Laboratory for running the Gearbox Reliability Project, the participants and organizers and the US Department of Energy for support of the GRC project.

This material is based on work supported in part by National Science Foundation grant (CBET-0933292). Any opinions, findings and conclusions or recommendations expressed are those of the authors and do not necessarily reflect the views of the NSF.