This article describes how we verified the strength of the blades of our small wind turbine by using the IEC 61400-2 standard.

Important Note

Preliminary content from design report

The content of this article is taken from the December 2013 preliminary design report. It represents intention of design at that stage but does not necessarily show the final version of the HOLI 300 turbine design.

The calculated forces and moments from the load cases have to be converted into equivalent component stresses to be compared with the material allowed stresses. The following points have to be considered for the calculation of the equivalent stresses:

• The stress level can be different along the component and show peeks
• Important are the stress flow and the directions
• Different sizes of the component and surface treatments, including any change of material due to manufacturing like welding or other actions.

The blade parameters for stress calculation are as follows.

$D=0.06\,\textrm{m}$
$d=0.038\,\textrm{m}$

$A_{\textrm{B}}=\frac{\pi(D-d)^{2}}{4}=3.8\cdot10^{-4}\,\textrm{m}^{2}$

Second moment of inertia for the blade root (for a circle):

$I_{\textrm{xyB}}=\frac{\pi(D^{4}-d^{4})}{64}=5.34\cdot10^{-7}\,\textrm{m}^{4}$

$c_{\textrm{B}}=0.03\,\textrm{m}$ (distance from centroid to point
of max. stress)

$W_{\textrm{B}}=\frac{I_{\textrm{xyB}}}{c_{\textrm{B}}}=1.78\cdot10^{-5}\,\textrm{m}^{3}$

The ultimate strength of the blade material chosen, PEEK HP3 Plastic, is $f_{\textrm{kB}}=90\,\textrm{MPa}$.

The partial safety factors for loads, according to Table 7 of IEC 61400-2, for the simple load calculation method, for fatigue loads is $\gamma_{\textrm{f-f}}=1.0$, and the partial safety factor for ultimate loads is $\gamma_{\textrm{f-u}}=3.0$.

The fully characterised partial safety factors from Table 6 of IEC 61400-2, were chosen to be used for the PEEK HP3 blade material. For fatigue and ultimate strength the partial material safety factors are $\gamma_{\textrm{m-f}}=10.0$ and $\gamma_{\textrm{m-u}}=3.0$ respectively. The fully characterised values were chosen to error on the side of caution.

The following equation will give the allowed equivalent stress for the different load cases for ultimate strength.

$\sigma_{\textrm{dB}}\leq\frac{f_{\textrm{kB}}}{\gamma_{\textrm{m-u}}\cdot\gamma_{\textrm{f-u}}}=\frac{90}{3\cdot3}=10.0\,\textrm{MPa}$

This value should not be exceeded in the following equivalent load case calculations.

### Equivalent stress for case A: Normal operation

This first load case is only fatigue load, but for further calculations it is also necessary to find the equivalent stress level for normal operation using the following equations [1].

Equivalent stress formula for axial load:

$\sigma_{\textrm{zB}}=\frac{\triangle F_{\textrm{zB}}}{A_{\textrm{B}}}=6.02\,\textrm{MPa}$

Equivalent stress formula for bending:

$\sigma_{\textrm{MB}}=\frac{\sqrt{\triangle M_{\textrm{xB}}^{2}+\triangle M_{\textrm{yB}}^{2}}}{W_{\textrm{B}}}=1.221\,\textrm{MPa}$

Combined (axial + bending – peak to peak variation):

$\sigma_{\textrm{eqB}}=\sigma_{\textrm{zB}}+\sigma_{\textrm{MB}}=7.24\,\textrm{MPa}$

It is assumed that the PEEK HP3 plastic would perform similarly to the Victrex 450G. Since the combined axial and bending stress of the blade is a peak to peak variation, and only the amplitude of the variation is shown on the S,N-diagram, the combined stress has to be divided by 2, and the material partial safety factor of 10 for fatigue has to be applied. With calculation of equivalent stress, $36.2\,\textrm{MPa}$ it can be determined that the material would collapse after $N\approx1\cdot10^{20}$ cycles.

$N\approx1\cdot10^{20}$ number of cycles to fail at the stress $s_{\textrm{i}}\cdot\gamma_{\textrm{m-f}}\cdot\gamma_{\textrm{f-f}}=36.2\,\textrm{MPa}$
$n_{\textrm{i}}=1.69\cdot10^{10}$ number of fatigue cycles
$s_{\textrm{i}}=3.62\,\textrm{MPa}$ Amplitude of maximum stress
$\gamma_{\textrm{m-f}}=10.0$ $\gamma_{\textrm{f-f}}=1.00$

$Damage=\sum\frac{n_{\textrm{i}}}{N\left(\gamma_{\textrm{m-f}}\cdot\gamma_{\textrm{f-f}}\cdot s_{\textrm{i}}\right)}=1.7\cdot10^{-10}\leq1.0$

### Equivalent stress for case B: Yawing

Equivalent stress formula for the blade root:

$\sigma_{\textrm{eq}}=\frac{\triangle M_{\textrm{yB}}}{W_{\textrm{yB}}}=5.17\,\textrm{MPa}$

### Equivalent stress for case C:Yaw error

Equivalent stress formula for only the bending moment on the blades:

$\sigma_{\textrm{eq}}=\frac{\triangle M_{\textrm{yB}}}{W_{\textrm{B}}}=1.12\,\textrm{MPa}$

### Equivalent stress for case E: Maximum rotational speed

$\sigma_{\textrm{eq}}=\frac{F_{\textrm{zB}}}{A_{\textrm{B}}}=9.59\,\textrm{MPa}$

### Equivalent stress for case F: Short load connection

$\sigma_{\textrm{eq}}=\frac{M_{\textrm{xB}}}{W_{\textrm{B}}}=0.76\,\textrm{MPa}$

### Equivalent stress for case G: Shutdown (Braking)

Equivalent stress formula for blade root:

$\sigma_{\textrm{eq}}=\frac{M_{\textrm{xB}}}{W_{\textrm{B}}}=0.99\,\textrm{MPa}$

$\sigma_{\textrm{eq}}=\frac{M_{\textrm{yB}}}{W_{\textrm{B}}}=3.55\,\textrm{MPa}$

### Summary

This wind turbine is facing different environmental conditions. The following table compares the calculated equivalent stresses at certain environmental impacts on the SWT with the allowed material stresses. Because we only used simplified equations in this load simulation, it is necessary to evaluate the SWT model in further field studies. So far all equivalent stresses are below the material stress limits. There are more environmental conditions than wind, which have an impact or an effect on the integrity of this SWT. It is assumed that the SWT is located in middle Europe with moderate temperature, humidity and solar radiation.

The results of load calculation are presented in the table below.

[1] IEC, “Wind turbines – part 2: design requirements for small wind turbines,” , iss. 61400-2, 2006.
[Bibtex]
@STANDARD{InternationalElectrotechnicalCommission2006,
title = {Wind turbines - Part 2: Design requirements for small wind turbines},
organization = {International Electrotechnical Commission},
institution = {TC/SC 88},
author = {{IEC}},
language = {English},
number = {61400-2},
revision = {2},
year = {2006},
owner = {helgehamann},
timestamp = {2013.12.15}
}