**A General Method for Fatigue Analysis of Vertical Axis Wind Turbine Blades***Paul S. Veers*, *October 1983*

The fatigue life of wind turbine blades that are exposed to the random loading environment of atmospheric winds is described with random data analysis procedures. The incident wind speed and the stresses caused by these winds are expressed in terms of probability density functions, while the fatigue life vs stress level relationship is treated deterministically. This approach uses a "damage density function" to express fatigue damage as a function of wind speed. By examining the constraints on the variables in the damage density expression, some generalizations of the wind turbine fatigue problem are obtained. The area under the damage density function is inversely related to total fatigue life. Therefore, an increase in fatigue life...

**An Approach to the Fatigue Analysis of Vertical Axis Wind Turbine Blades***Paul S. Veers*, *September 1981*

A cursory analysis of the stress history of wind turbine blades indicates that a single stress level at each wind speed does not adequately describe the blade stress history. A statistical description is required. Blade stress data collected from the DOE/ALCOA Low Cost experimental turbines indicate that the Rayleigh probability density function adequately describes the distribution of vibratory stresses at each wind speed. The Rayleigh probability density function allows the distribution of vibratory stresses to be described by the RMS of the stress vs. time signal. With the RMS stress level described for all wind speeds, the complete stress history of the turbine blades is known. Miner’s linear cumulative damage rule is used...

**Effects of Cyclic Stress Distribution Models on Fatigue Life Predictions**

*Herbert J. Sutherland and Paul S. Veers, Wind Energy, 1995, pp. 83-90 *

The fatigue analysis of a wind turbine component typically uses representative samples of cyclic loads to determine lifetime loads. In this paper, several techniques currently in use are compared to one another based on fatigue life analyses. The generalized Weibull fitting technique is used to remove the artificial truncation of large-amplitude cycles that is inherent in relatively short data sets. Using data from the Sandia/DOE 34m Test Bed, the generalized Weibull fitting technique is shown to be excellent for matching the body of the distribution of cyclic loads and for extrapolating the tail of the distribution. However, the data also illustrate that the fitting technique is not a substitute for an adequate data base.

**Fatigue Case Study and Reliability Analyses for Wind Turbines***Herbert J. Sutherland and Paul S. Veers*, *Sandia National Laboratories, **1995*

Modern wind turbines are fatigue critical machines used to produce electrical power. Economic viability requires them to have both low initial cost and long term reliability. The Fatigue and reliability projects in Sandia's Wind Energy Program are developing the analysis tools required to accomplish these design requirements. The first section of the paper formulates the fatigue analysis of a wind turbine using a cumulative damage technique. The second section uses reliability analysis for quantifying the uncertainties and the inherent randomness associated with turbine performance and the prediction of service lifetimes.

**Fatigue Life Variability and Reliability Analysis of a Wind Turbine Blade**

*Paul S. Veers, **Herbert J. Sutherland, Thomas D. Ashwill, Sandia National Laboratories*

Wind turbines must withstand harsh environments that induce many stress cycles into their components. A numerical analysis package is used to illustrate the sobering variability in predicted fatigue life with relatively small changes in inputs. The variability of the input parameters is modeled to obtain estimates of the fatigue reliability of the turbine blades.

**Predictions of peak fatigue stresses in a Darrieus rotor wind turbine under turbulent winds**

*D.J. Malcolm, Proceedings of 9th ASME Wind Energy Symposium, New Orleans, January 1990*

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The field stress data from two locations on the blade of the Indal 500 kW Darrieus rotor have been processed into histograms of fatigue stresses and grouped according to the atmospheric turbulence intensity. The aim was to determine the magnitude of the maximum cyclic stresses on the rotor. These distributions are compared with corresponding results obtained from a frequency domain structural analysis model. Comparisons are good and confirm the greater role of turbulence in in-plane blade bending.

**The LIFE Computer Code Fatigue Life Prediction for Vertical Axis Wind Turbine Components***Herbert J. Sutherland, Thomas D. Ashwill, Norman Slack, Sandia Report, August 1987*

The LIFE computer code was originally written by Veers to analyze the fatigue life of a vertical axis wind turbine (VAWT) blade. The basic assumptions built into this analysis tool are: the fatigue life of a blade component is independent of the mean stress; the frequency distribution of the vibratory stresses may be described adequately by a Rayleigh probability density function; and damage accumulates linearly (Miner's Rule). Further, the yearly distribution of wind is assumed to follow a Rayleigh distribution. The original program has been updated to run in an interactive mode on a personal computer with a BASIC interpreter and 256K RAM. Additional capabilities included in this update include: the generalization of...