Rotating bearings are some of the most commonly employed machine elements. As such, they are well-understood and thoroughly researched pieces of technology. Fatigue lifetime calculation is internationally standardized through ISO 281, which is based on the assumption that loads act on a bearing under constant rotation. Blade bearings of wind turbines do not conform to this assumption since their movement typically consists of small, repetitive oscillations. Moreover, their load distribution differs considerably over the bearing circumference, a load case for which ISO 281 refers to ISO 16281 and which requires detailed simulations of the bearing to be sufficiently precise. Aside from ISO 16281, the NREL DG03, a guideline for pitch and yaw bearing lifetime, lists two methods for incorporating bearing loads into the fatigue life calculation. This paper compares all three methods. Two of the methods can not be used directly for the double-row four-point bearing used in this paper and are thus slightly adjusted. Load distributions in the bearing are simulated and curve-fit by means of a novel approach using regression analysis. The method from NREL DG03, which requires the least computational effort, is shown to result in a much higher lifetime than the other two, which are based on internal load distributions of the bearing. The two latter methods are shown to produce very similar results. An adjustment is proposed for increasing the accuracy of that lifetime calculation method which requires the least computational effort in order to resemble the other two more closely.

Blade bearings are a critical component of any modern wind turbine. Enabling the turbine to pitch can reduce the loads on a multitude of its components significantly. This allows components to have a lighter design and a higher return on investment of the entire machine.

Apart from continuous pitch control (CPC), which turns all blades simultaneously by the same angle, individual pitch control (IPC) has been the subject of comprehensive research (e.g.,

Bearings exhibit a vast number of possible failure mechanisms, including fatigue, fretting corrosion, brinelling, false brinelling, and more

ISO 281 is intended for bearings under continuous rotation subjected to a constant axial and radial load or a combination thereof. To account for more complicated load situations, ISO 16281

Even with these standards in place, a great deal of uncertainty remained with regards to the calculation of pitch bearing lifetime. While ISO 16281 allows for consideration of the complicated load situation caused by a tilting moment, oscillatory movement patterns have yet to be considered in any of the standards. Moreover, large slewing bearings behave somewhat differently from the smaller ones on which the standard is primarily based. In 2009, the NREL (National Renewable Energy Laboratory, USA)

Moreover, failure modes of blade bearings are manifold and not just limited to fatigue (see

The present uncertainty is reflected by the certification demands of manufacturers. In its 2003 Guideline for the Certification of Wind Turbines

The present paper examines different lifetime calculation methods from the abovementioned standards and guidelines and compares them to each other in order to highlight differences in the methods and their results. First, the simulations underlying the present paper and the calculation methods used herein are explained in detail. Then, results of the methods presented are compared and discussed.

The calculation methods presented herein are intended for a double-row four-point contact ball bearing in a nearshore wind turbine. Turbine loads are simulated according to International Electrotechnical Commission (IEC) 61400-1

Simulations of the time series were carried out using the IWES Wind Turbine IWT-7.5, a wind turbine model designed by Fraunhofer IWES and described by

Main turbine properties of IWT-7.5

FE model of blade, bearing, and hub.

The model assumes that the turbine operates with a controller designed
by the German wind turbine manufacturer Enercon. Enercon used the aeroelastic model
of the IWT-7.5, equipped with their own IPC controller, to run load simulations. This
controller is a wideband IPC, designed to minimize loads as much as possible without
limiting the movements of the pitch bearing. The Enercon IPC activates at wind speeds slightly below rated speed. This speed region contributes a large
share to the overall fatigue loads of the turbine. The control values are the loads in a nonrotating hub coordinate system, and the main objective is to minimize loads on
the steel structures of the turbine (hub, machine frame, tower).

Aeroelastic simulations of the wind turbine were carried out according to IEC 61400-1, DLC1.1. A total of 20 years of lifetime were simulated. The calculated loads and movements of one bearing are used as input for the subsequent calculations.

Available literature on the analysis of time series with oscillatory movement patterns is sparse. Fatigue lifetime calculations are most commonly done using a rain flow count

After a rain flow cycle count of the bearing oscillations, the results were further divided into bins of the resulting tilting moment, its angle, and the absolute pitch angle of the bearing using the procedure described by

The generation of the entire FE model as well as all simulations was performed using Ansys R3. For all FE simulations, a one-third rotor star FE model was used. It consists of a rotor blade, one-third of a rotor hub, a pitch bearing, and a stiffener plate. Using only a one-third rotor star model greatly reduces the computational effort. Doing so makes the model behave symmetrically, meaning that it is not possible to simulate different loads acting on the three blades, a process which is assumed to have negligible effects on the loads of one bearing. Part of the model is shown in Fig.

The outer ring of the bearing connects directly to the blade flange of the hub. The bearing’s inner ring connects to the blade with the stiffener plate in-between. Using stiffener plates is a common way to reduce the ovalization of the bearing, which is caused by the blade. The stiffener plate is made of steel and has a thickness of 25 mm, which is a typical thickness for a blade flange of that size. The blade model contains a fully modeled root section. The component contacts are simulated to be bonded over the connecting surfaces, meaning that no bolts and friction-based contact behavior are implemented.
Not implementing bolts might lead to a little more flexibility of the bearing rings, which can result in a larger tilting of the rings towards each other. In turn the loads on both rows are distributed slightly less evenly. In-house investigations have shown that this effect only has a very small influence on the bearing's load distribution. Thus, the effect of this simplification is to be assumed negligible.
The model is completely fixed at the hub's rotor flange (downwind) and partially fixed at the hub's upwind flange. In addition, cyclic constraints at the hub's one-third cutting planes are implemented. All these boundary conditions enable a realistic deformation behavior of the rotor hub to be modeled. The loads are applied to the blade's spar caps at a blade length of 40 m. Concentrating all loads acting on a blade at one point is a common method for determining bearing loads that does not completely reflect the load application on a real blade. In-house investigations beforehand have shown that doing so delivers comparable results to a realistic load application as long as the load application point is not located in the first quarter of the blade. Figure

Bearing ring deformation in meters for the load case

The bearing used for all simulations is a double-row four-point contact ball bearing as described in

Main properties of blade bearing investigated (cf.

Bearing cross section and raceway definitions.

The balls of the bearing are not fully modeled but represented by nonlinear springs, which is a common approach according to

During the aeroelastic simulations performed for the lifetime simulations of the turbine, a wide variety of different loads act on the pitch bearings. Of these, the three most influential factors are the resulting tilting moment

Coordinate system and angle definitions.

Contact forces are thus simulated at a discrete number of points using 358 different combinations of

All combinations of pitch angle

All the standards and guidelines mentioned in Sect.

Firstly, an equation based on the applied tilting moment is given as

As a more sophisticated approach, the DG03 also lists

Note that the variable

As a third approach, the individual lifetime of each raceway is calculated according to ISO 16281. Like NREL 2, this approach is based on individual rolling-element loads. Equivalent loads

The basic rating life

A number of approaches exist for factoring in the movement patterns of bearings (see

Low rotational speeds worsen lubrication conditions, which, in turn, reduces the fatigue lifetime of a bearing. ISO 281 proposes an approach based on the multiplication of the basic rating life

First, the approach for contact force regression analysis used herein is verified. Thereafter, the results of all three lifetime calculation methods listed in Sect.

As depicted in Fig.

Equation (

Figure

Forces

Likewise, the pitch angle affects the contact force as shown in Fig.

Forces

The degree of

After regression analyses have been done for each

FE-simulated (solid lines) and interpolated (dashed lines) forces

A bin counting is carried out in order to calculate the lifetime of the bearing. For 54 different bins of the oscillation angle, the three variables moment

Dots for each chosen class occurring during aeroelastic simulations, with size relative to frequency of occurrence.

For each of the bins, the equivalent load is determined according to the three variants laid out in Sect.

Equivalent loads

With a constant moment of

The difference between the maximum and minimum of the two methods is then approximately

Equivalent loads

Differences in equivalent loads between NREL 2 and ISO 16281 decrease with an increase in the moment, as shown in Fig.

Equivalent loads

Other operating points not shown in Figs.

Using these values, the overall lifetime of the bearing

These calculated lifetimes are significantly below the expected lifetime of a wind turbine of 20 years. This discrepancy is similar to other publications on the issue (cf.

Assessing the exact reasons for the differences between calculation and reality is, however, difficult. Calculation methods are largely based on research with small bearings, whose conditions during manufacturing and operation differ from those of large slewing bearings (cf.

Fatigue lifetimes of all methods investigated.

Given the fact that the qualitative behavior of NREL 1 closely resembles that of the other two methods, as can be seen in Fig.

Fatigue lifetimes of all methods investigated.

Blade bearings of wind turbines operate under unusual operating conditions compared to others in the industry. Some details which go beyond the internationally standardized calculation of fatigue lifetime as per ISO 281, such as the calculation of equivalent loads or the consideration of oscillatory behavior, can thus be obtained by a number of methods. This paper investigated three different approaches for the calculation of equivalent loads

For the case of a blade bearing of the reference wind turbine, load distributions in the bearing have been simulated and curve fit to allow for consideration of a variety of operating points. The results show that changes in the load and pitch angle of a rotor blade bearing lead to significant changes in the equivalent load

The two methods that calculate

As already seen in other publications on the fatigue lifetime calculation of pitch bearings, these results are far lower than the expected lifetime of a turbine of 20 years. Many reasons may account for this discrepancy: calculation methods are largely based on research with small bearings, whose conditions during manufacturing and operation differ from large slewing bearings. Effects such as the changing contact angle during operation that occurs for large slewing bearings with flexible attached structures are not considered at all. Moreover, the effect of

FE-simulated bearing loads have been uploaded to

OM carried out all calculations unless stated otherwise. MS wrote the tools used for data analysis and provided the idea for contact force regression analysis. FS prepared and carried out all FE simulations.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Wind Energy Science Conference 2019”. It is a result of the Wind Energy Science Conference 2019, Cork, Ireland, 17–20 June 2019.

Lifetime simulations of the wind turbine were created using a pitch controller from Enercon.

This research has been supported by the German Federal Ministry for Economic Affairs and Energy (grant no. FKZ: 0325918A).

This paper was edited by Carlo L. Bottasso and reviewed by Carlo Gorla and Jonathan Keller.