3D REFERENCE MODEL FOR BEARING CONNECTIONS OF WIND TURBINE COMPONENTS 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: email@example.com, M.vanDuijvendijk@mecal.nl www.mecal.nl Figure 1: Pitch bearings in the wind turbine rotor Summary 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 bearing. 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 results 3. 3D section and full 3D model with fixed End point: contact angle. Accurate 3D bearing model In reference , 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 connections. Relative axial displacement inner raceway Displacements Figure 5: Detailed view on deformations of 3D model 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 results. 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 components. 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  Frese, Thomas. Dalhoff, Peter. Fatigue analyses of bolted and welded joints. Germanischer Lloyd. Nafems seminar, 8-9 November 2000, Wiesbaden, Germany 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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