Kalverboer, A.F., Gruiter, T.J.D. de, Duijvendijk, M. van
                 Mecal Applied Mechanics BV, P.O. Box 286, 7500 AG Enschede, the Netherlands,
                               tel. ++31 (0)53 4821400, fax. ++31 (0)53 4821401,
                          e-mail: a.kalverboer@mecal.nl, M.vanDuijvendijk@mecal.nl

                                 Figure 1: Pitch bearings in the wind turbine rotor

Modern wind turbines generally have pitchable blades, which enable adjustments to changes in wind conditions. The
bearings that connect the blades to the hub are a critical part of the wind turbine. Current models to calculate the
behaviour and strength of these bearing connections are generally simplified and not sufficient to predict its strength
for all load conditions accurately. To overcome this problem, an accurate model is required that incorporates all
relevant aspects of the bearing and the connected parts. The accuracy of the model is verified with measurements.

KEYWORDS: 3D, bearing, accuracy, FEM, simulations, verification, wind turbine components

1.   Introduction                                               2.   2D axi-symmetric harmonic model

Current models to calculate the behaviour and                   Mecal has successfully employed an axi-symmetric
strength of bearing connections are generally                   harmonic model for several years now.
simplified representations and often in 2D, or in 3D
section models (see chapter 2 and 3). General
assumptions are: linear material behaviour, no or
uniform gapping of attached components and
constant pressure angles over circumference for
bearing balls. Generally these simple models are only
valid when the behaviour is linear (no gapping etc).
From practice however it is known that material
behaviour is not linear, gapping between components
occurs and pressure angles vary depending on load               Figure 2: 2D axi-symmetric harmonic model
size and direction. Therefore, for describing the non-
linear behaviour the current models do not suffice and
more sophisticated models are required.                         Characteristics of this model are:
                                                                •   Axi-symmetric geometry of bearing and
This paper describes the realisation of the 3D bearing              attached components.
model. The model is developed in several steps to               •   Harmonic loading on model to represent varying
assure reliable, realistic and predictable output.                  contact angle over the circumference of the
First, a short overview of earlier models is presented,         •   Gapping of the connection occurs on full
then the 3D reference model is described together                   circumference; this results in conservative bolt
with its validation, followed by the field of                       stresses.
application and conclusions.
•    The model is very efficient with respect to         The model was built in several stages as displayed
     calculation time and therefore an indispensable     below, to assure a quantifiable and reliable output:
     design tool.
•    The choice of model simplifications leads to
     conservative results and possibly to                                        Starting point:
     over-dimensioning of components.                                           2D harmonic axi-
                                                                                symmetric model

                                                                  2D axi-symmetric sphere-
                                                                   spherical socket model
                                                                   Comparison with hertz

                                                                   3D bearing section model
                                                                    Comparison with Nachi

                                                                      3D bearing model
                                                                      Comparison with
Figure 3: 2D axi-symmetric model deformation                         measurement values

3.   3D section and full 3D model with fixed                                    End point:
     contact angle.                                                     Accurate 3D bearing model
In reference [1], Germanischer Lloyds (GL) presents
two models of the blade hub connection: a 3D section
model and a 3D full model. The characteristics of        Mecal created a 3D reference finite element model
both models are:                                         which incorporates the bearing and connected
                                                         components with a high level of detail. Non-linear
•    Blade and hub are modelled in axi-symmetric         phenomena like gapping, contact behaviour and non-
     geometry, with boundary conditions at some          linear material properties are included.
     distance from bearing.
                                                         4.1 3D full model
•    Bearing balls and contact behaviour is modelled
                                                         Characteristics of this model are:
     with spring elements. The contact angle is fixed
     at a conservative contact angle. The elements are   •   Three-dimensional solid model, allowing for
     aligned in a cross per rolling element, perhaps         complex geometry of attached components.
     'compression-only' elements are used. The           •   Incorporation of all bearing balls and raceways,
     accuracy of the contact behaviour, linear or non-       allowing for (self-adjusting) varying contact
     linear is unknown.                                      angle over the circumference of the bearing.
•    Non-linear contact between bearing and attached     •   Non linear contact between bearing and attached
     components, allowing for realistic gapping of           components, allowing for realistic gapping of
     the connection.                                         the connection.
                                                         •   The model is highly non-linear and therefore
In the 3D section model, only half a single bolt             calculation time consuming.
segment is modelled in combination with symmetry         •   High level of detail leads to accurate results
conditions.                                                  under all circumstances.

GL concludes: The segment model results are
conservative since they show the highest bolt forces.
The full modelled flange shows very good agreement
with measured forces for low external bending
moment and satisfying agreement for higher loads.

4.   3D reference model

To improve the calculation method, Mecal has
created an all-embracing finite element model of the
pitch bearing connection. This model serves as a
reference model for more efficient design tools.
Mecal’s 3D-reference model includes virtually all        Figure 4: Detailed view on part of 3D model
mechanical phenomena typical for bearing
                                                                           Relative axial displacement inner raceway

Figure 5: Detailed view on deformations of 3D

                                                                                         Bending moment
4.2 Validation
The reference model is validated using theoretical
cases and measurements. Contact behaviour is              The results of the 3D bearing reference model are still
validated with Hertz contact formulae, where Hertz        on the conservative side and much closer to reality
theory is valid. Influences of element size and contact   than the 2D-axi symetric model
parameters were studied in combination with
convergence speed, calculation time and accuracy of       5.              Application field
                                                          From the detailed and validated FEM model
The 3D full bearing deformations with rigid               simplified models can be deduced, with all required
boundaries are compared with Nachi formulae for           capabilities, depending on specific requirements. For
deformations of deep groove ball bearings.                verification of these simple models the 3D reference
                                                          model can be used.

                                                          By creating an all-embracing model, more
                                                          understanding can be gained about the behaviour of
                                                          bearings and they way to model this behaviour with
                                                          sufficient accuracy. This will lead to more (cost)
                                                          efficient designs of the bearings and the attached

Figure 6: Bearing model with rigid boundaries             Besides looking at one-single blade hub connection,
                                                          the bearing model can be used to determine the
And the 3D bearing model connected to a wind              interaction between 2 or 3 blades
turbine blade is compared with measurements on an
equal test set-up.                                        The derived knowledge can also be applied to
                                                          yaw-bearing connections.

                                                          5.              Conclusions

                                                          The validated 3D-reference model can be used to
                                                          design reliable and cost-efficient bearing connections
                                                          and attached components.

                                                          6.              References

                                                          [1] Frese, Thomas. Dalhoff, Peter. Fatigue analyses
                                                          of bolted and welded joints. Germanischer Lloyd.
                                                          Nafems seminar, 8-9 November 2000, Wiesbaden,
Figure 7: 3D Simulation model of test set-up
                                                          Mecal offers straightforward design and innovation,
An exemplary result between the 3D-axi-symetric           high-tech engineering and verification in the field of
harmonic model, the 3D full reference model and           dynamic, mechanic and structural wind turbine
measurements is displayed below.                          technology.

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