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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Innovative concepts for drive train components' taking place on Thursday, 13 March 2014 at 11:15-12:45. The meet-the-authors will take place in the poster area.

Håkan Johansson Chalmers University of Technology, Sweden
Co-authors:
Håkan Johansson (1) F P Viktor Berbyuk (1)
(1) Chalmers University of Technology, Göteborg, Sweden

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Presenter's biography

Biographies are supplied directly by presenters at EWEA 2014 and are published here unedited

Dr. Johansson is Lecurer in Mechanical Systems at the division of Dynamics, Dept. of Applied Mechanics since 2010. He is resarch topics include wind turbine drive trains, fatigue analysis, numerical methods and optimization. He is active within the Swedish Wind Power Technology Center SWPTC.

Abstract

Statistical analysis of fatigue loads in a direct drive wind turbine

Introduction

In the design of wind turbines, a large number of simulations of wind turbine dynamics response are carried out. In order to assess the fatigue life of drive train components, simulations are carried out at different wind speed, and for each wind speed the a partial damage is estimated, and the total damage is obtained by a summation for all wind speeds weighted by the wind speed distribution. The purpose of this contribution is to assess the variability of this estimated damage with respect wind turbulence model, number of simulations and wind speeds, and drive train model assumptions.

Approach

A model for a multi-MW direct drive wind turbine was developed using the software ViDyn [1] developed by Teknikgruppen AB. The wind fields are random realizations based on the Kaimal spectra as described in the standard IEC-61400 [2] characterized by turbulence intensity, wind shear etc. Each such wind field realization is used as input to the model complete-turbine (including realistic pitch control) from which the forces at the hub is extracted. These forces are thereafter used as input to a drive train model developed in Matlab. From this drive train model, the rate of bearing fatigue is estimated at four bearings along the main shaft; Front and Rear main bearings and Front and Rear generator stator support bearings.
Due to the randomness of the wind field, a number of simulations are carried out to estimate the variability of bearing fatigue rate, and how this rate varies with mean wind speed. The variability is studied with respect to turbulence intensity and drive train model detail.
To assess the total damage in bearings, a simple approach is to use a fixed number of realizations at each integer wind speed within the range of operation, and the total damage is obtained by a summation for all wind speeds weighted by the wind speed distribution. However, since the variability of damage rate depends on the wind speed, and the wind speed distribution is not uniform, we seek to study and modify the “sample” of turbine simulations carried out based on knowledge of the wind speed distribution and how the damage rate depend on the wind speed to obtain as reliable estimate of the variability as possible.


Main body of abstract

With the aim to consider different drive train models fidelity, a direct drive turbine model is considered as represented in Figure , where the main shaft is represented by an Euler-Bernoulli beam, added with point inertias representing hub and generator rotor in a rotating coordinate system, supported by linear springs representing flexibility in bearings and bearings mounts. The weight of the stator is carried by the main shaft via bearings (also represented by linear springs), while the torque support between the generator stator and the bedplate is represented by a torsional spring, see idealized Figure .
The excitation from wind is represented by a force vector (forces in xyz-direction and moments around the same axes) acting on the hub. To get a reasonably realistic load, the software ViDyn [1] was used to compute hub forces for given realizations of wind field according to IEC standard. From a 10-minute simulation at a specified mean wind speed, the time-history of forces acting on the main shaft bearings are computed, from which a mean damage rate is determined according to standard bearing fatigue calculation (the varying loads are summed according to the Palmgren-Miner rule).
For 25 simulations at each wind speed, the mean damage rate for the front and rear main bearing is shown in Figure , and as a measure of variability, the standard deviation is shown in the same figure. For the front main bearing, it is seen that the largest damage rate, as well as the largest variability arise at 11 m/s, which is the region where rotor blade pitch control starts. For the rear main bearing, the damage and variability increase for increased mean wind speed, Figure . The front and rear generator stator bearings give very similar results, only the front bearing damage rate is shown in Figure . Here the largest rate is for high wind speed, but the largest variability seems to be linked to the pitch control.
A comparison has been made regarding the influence of modeling detail. Three choices of model detail are here considered with respect to mean and variance of damage rate. Firstly the quasi-static condition is considered, i.e. inertia effects are ignored. Secondly, since a direct drive the main shaft operates under relatively modest speed, 5-15 rpm, the centrifugal and gyroscopic terms in the equations of motions could possibly be ignored. Finally the complete dynamics model including inertia and gyroscopic terms is considered. A comparison for the front and rear main bearing is shown in Figure , where it can be concluded that a quasi-static drive train model is sufficient to predict damage rate for those bearings. In contrast, as shown in Figure , inertia effects (but not necessarily gyroscopic and centrifugal effects) should be considered to predict the damage rate of the stator bearings.
A sometimes adopted model simplification is to lump together the generator rotor and stator as one point inertia. It was also numerically found that the estimated damage rate on the main bearings was unaffected of this simplification, which appears reasonable since the forces affecting the main bearings are essentially quasi-static. In such case, the stator bearings must be investigated separately.


Conclusion

It was found that model detail can for some cases affect the estimated damage rate, depending on the specific concept of turbine drive train. For the direct drive concept studied here, a quasi-static model was sufficient to predict the damage rate for the main bearings that carry the drive train weight and wind thrust load, whereas the stator bearings that carry a the stator mass require inertia to be considered. Moreover it was found that the not only the mean, but also the variance of damage rate depend on mean wind speed. From inspection it was found that the estimated damage is essentially normally distributed, although some non-zero higher order moments was found.
Future work will in more detail study the efficient sampling of wind turbine simulations to estimate mean and variability of predicted damage in the turbine drive train components with sufficient accuracy. Considering the front main bearing, it seems that wind speeds around 11 m/s requires most attention, whereas for the rear main bearing it is not likewise obvious as high wind speeds are significantly less frequent. Moreover, additional cases with respect to turbulence characteristics will be presented. Following this, more elaborate wind models should be studied, in particular with respect to wakes in the wind field that may appear randomly in the swept area.
Here, the model of the drive train was decoupled from the full-turbine model. Therefore a future important step is to include also the more elaborate model within the full-turbine analysis code. However, this requires an essentially new simulation platform, one such is currently under development at our department (tentatively named FreeDyn).



Learning objectives
This presentation will help designers to reduce the number of simulations needed for certification, or alternatively, to ensure that the chosen simulations give best precision in the fatigue estimation.


References
[1] H. Ganander. The use of a code-generating system for the derivation of the equations for wind turbine dynamics. Wind Energy, 6(4) 333-345, 2003
[2] International electrotechnical commission (IEC) Standard. 61400 Wind turbines – part 1: Design requirements, 2005