In this section we specify the load assumptions for our HOLI 300 turbine under the conditions of the IEC 61400-2 Rev. 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.

### Specification of Design Load Cases

The load calculation for a SWT (Small Wind Turbine) can be done in several ways. One way is to test the model for all kinds of conditions, which implies that the SWT is built as a prototype already. In our case several load cases and high safety factors will be used to show that the parts which take the highest forces can withstand these conditions. These parts will be the main shaft, transporting the torque to the generator and the bending moments at the blade root. The IEC (International Electrical Committee )standard for SWT [1] defined a so called “simplified load model” which can be used for horizontal axis wind turbines (Horizontal Axis Wind Turbines HAWT) with two or more blades and a rated power lower than 50 Kilowatts. If the rotor swept area is smaller or equal to 2 m², it is allowed to certify the turbine and the tower individually. In this case, the tower will be provided and will not be part of this calculation. The different load cases are described in the table below whereas “F ” stands for the analysis of fatigue loads and shall be used for the assessment of fatigue strength calculations and “U” stands for ultimate loads, which should be referred to the maximum strength of the material.

### Coordinate System

The following coordinate system originating from the before mentioned IEC standard will be used in the load calculations.

\subsection{Specification of Design Conditions\label{sub:Specification-of-Design} }

The specified design conditions are related to the location of our proposed wind turbine as well as the design specifications determined by the contest hosts. The following list summarizes the requirements:

• Rotor area $A\leq2\,\textrm{m}^{2}$ (equivalent for the maximum diameter of $\phi=1.6\,\textrm{m}$ )
• $z_{\textrm{hub}}=10\,\textrm{m}$
• $v_{\textrm{ave}}=4.0\,\frac{\textrm{m}}{\textrm{s}}$ at standard atmospheric conditions

To ensure the durability and the safety of our SWT, we have to specify it according to the IEC standards for SWT [1]. To cover most of the varying wind conditions for a chosen location, the IEC standard has implemented a table of different wind classes, which are representing plausible wind speeds at certain occasions like the 50-year gust or the turbulence intensity. The SWT should be able to withstand these extreme conditions and it is the necessity of the turbine manufacturer to prove this in form of load and structural integrity calculations. The following table shows the different wind classes, according to the IEC standards [1]:

Basic parameters for SWT classes
SWT ClassUnitIIIIIIIVS
$V_{\text{ref}}$m/s5042.537.530(*)
$V_{\text{ave}}$m/s108.57.56(*)
I1510.180.180.180.18(*)
a12222(*)

(*): Values to be specified by the designer

To meet the required wind conditions and to not do our own specification like in wind class S, which actually should be used for offshore or tropical storm regions, our design team chose SWT class IV for the load and structural integrity calculations.

As design conditions we chose wind conditions according to IEC IV [1] and an operating temparture range of $-20\ldots+40\text{°}\textrm{C}$. These are the HOLI 300 specifications for the design load calculations:

• Design RPM $n_{\textrm{design}}=400\,\textrm{RPM}$
• Max. RPM $n_{\textrm{max}}=715\,\textrm{RPM}$
• Design wind speed $V_{\textrm{design}}=1.4\cdot V_{\textrm{ave}}\approx8.4\,\textrm{m/s}$ where $V_{\textrm{ave}}=6\,\frac{\textrm{m}}{\textrm{s}}$
• Design shaft torque $Q_{\textrm{design}}=\frac{30P_{\textrm{design}}}{\eta\pi n_{\textrm{design}}}=14.34\,\textrm{Nm}$ where $P_{\textrm{design}}=362\,\textrm{W}$
• Maximum yaw rate $\omega_{\textrm{yaw,max}}=3\,\frac{\textrm{rad}}{\textrm{s}}$ for
$A_{\textrm{proj}}<2\textrm{\,\ \ensuremath{m^{2}}}[/latex]
• Design tip speed ratio [latex]\lambda_{\textrm{design}}=\frac{R}{V_{\textrm{design}}}\frac{\pi n_{\textrm{design}}}{30}=3.99$

#### Load case A: Normal operation

For the normal operation mode [1] we calculate forces for further fatigue load calculations. At first the blade loads are calculated.

Centrifugal force at the blade root (z-axis):
$m_{\textrm{B}}=1.856\textrm{\,\ kg}$
$R_{\textrm{cog}}=0.350\textrm{\,\ m}$
$\omega_{\textrm{n,design}}=\frac{\pi n_{\textrm{design}}}{30}=41.94\textrm{\,\ rad/s}$

$\triangle F_{\textrm{zB}}=2m_{\textrm{B}}R_{\textrm{cog}}\omega_{\textrm{n,design}}^{2}=2286.99\,\textrm{N}$

Edge wise root bending moment (x-axis):

$Q_{\textrm{design}}=14.34\,\textrm{m}$
$B=4$
$g=9.81\,\textrm{m/\ensuremath{s^{2}}}$

$\triangle M_{\textrm{xB}}=\frac{Q_{\textrm{design}}}{B}+2m_{\textrm{B}}gR_{\textrm{cog}}=16.34\,\textrm{Nm}$

Flap wise root bending moment (y-axis):
$\lambda_{\textrm{design}}=3.99$

$\triangle M_{\textrm{yB}}=\frac{\lambda_{\textrm{design}}Q_{\textrm{design}}}{B}=14.32\textrm{\,\ Nm}$

The shaft load for fatigue stresses will be calculated at the first
bearing, which is closest to the rotor.

Thrust on shaft (x-axis):

$R=0.8\textrm{\,\ m}$

$\triangle F_{\textrm{x-shaft}}=\frac{3}{2}\frac{\lambda_{\textrm{design}}Q_{\textrm{design}}}{R}=107.41\,\textrm{N}$

$m_{\textrm{r}}=10.423\textrm{\,\ kg}$
$e_{\textrm{r}}=0.004\,\textrm{m}$ (eccentricity)

$\triangle M_{\textrm{x-shaft}}=Q_{\textrm{design}}+2m_{\textrm{r}}ge_{\textrm{r}}=15.16\,\textrm{Nm}$

Shaft moment (Bending moment):

$L_{\textrm{rb}}=0.05\,\textrm{m}$ (distance rotor to bearing)

$\triangle M_{\textrm{shaft}}=2m_{\textrm{r}}gL_{\textrm{rb}}+\frac{R}{6}\triangle F_{\textrm{x-shaft}}=24.55\textrm{\,\ Nm}$

In the next load case we only calculate the ultimate loads [1]
that occur during yawing with the maximum yaw speed at the design
rotational speed.

Flap wise root bending moment (y-axis):

$\omega_{\textrm{yaw,max}}=3\,\textrm{rad/s}$
$L_{\textrm{rt}}=0.163\,\textrm{m}$ (distance rotor to yaw axis)
$I_{\textrm{B}}=0.305\,\textrm{kgm}^{2}$

$\triangle M_{\textrm{yB}}=m_{\textrm{B}}\omega_{\textrm{yaw,max}}^{2}L_{\textrm{rt}}R_{\textrm{cog}}+2\omega_{\textrm{yaw,max}}\cdot I_{\textrm{B}}\omega_{\textrm{n,design}}+\frac{R}{9}\triangle F_{\textrm{x-shaft}}=87.25\,\textrm{Nm}$

The load on the shaft during yawing is related to the number of blades.
The equation for a three bladed turbine is.

Bending moment on the shaft:

$L_{\textrm{rb}}=0.05\,\textrm{m}$ (distance rotor to bearing)

$M_{\textrm{shaft}}=B\omega_{\textrm{yaw,max}}\omega_{\textrm{n,design}}I_{\textrm{B}}+m_{\textrm{r}}gL_{\textrm{rb}}+\frac{R}{6}\triangle F_{\textrm{x-shaft}}=172.93\,\textrm{Nm}$

#### Load case C: Yaw error

The turbine might not always be in the right yaw position so in case of a yaw error it is assumed, that the yaw angle is out by 30° [1]. The following equation calculates the resulting bending moment.

Flap wise root bending moment (y-axis):

$\rho=1.225\,\frac{\textrm{kg}}{\textrm{m}^{3}}$
$A_{\textrm{proj,}\textrm{B}}=0.0975\,\textrm{m}^{2}$
$C_{\textrm{l,max}}=1.06$

$M_{\textrm{yB}}=\frac{1}{8}\rho A_{\textrm{proj,B}}C_{\textrm{l,max}}R^{3}\omega_{\textrm{n,design}}^{2}\cdot\left[1+\frac{4}{3\lambda_{\textrm{design}}}+\left(\frac{1}{\lambda_{\textrm{design}}}\right)^{2}\right]=19.96\,\textrm{Nm}$

#### Load case D: Maximum thrust

The rotor shaft of the SWT can be exposed to a high load which acts parallel from the blades into the shaft [1]. This normal force can be calculated as follows.

Maximum thrust on shaft:

$C_{\textrm{T}}=0.5$
$v_{\textrm{ave}}=6\,\textrm{\ensuremath{\frac{\textrm{m}}{\textrm{s}}}}$

$F_{\textrm{x-shaft}}=c_{\textrm{T}}\frac{1}{2}\rho\left(2.5\cdot v_{\textrm{ave}}\right)^{2}\pi R^{2}=138.54\,\textrm{N}$

#### Load case E: Maximum rotational speed

This load case calculates the forces that appear in the root of the blade and due to the eccentricity the bending moment that takes effect on the shaft [1].

Centrifugal force at the blade root (z-axis):

$\omega_{\textrm{n,max}}=\frac{\Pi n_{\textrm{max}}}{30}=74.87\:\textrm{rad/s}$

$F_{\textrm{zB}}=m_{\textrm{B}}\omega_{\textrm{n,max}}^{2}R_{\textrm{cog}}=3644.25\,\textrm{N}$

Bending moment on the shaft:

$M_{\textrm{shaft}}=m_{\textrm{r}}gL_{\textrm{rb}}+m_{\textrm{r}}e_{\textrm{r}}\omega_{\textrm{n,max}}^{2}L_{rb}=16.80\,\textrm{Nm}$

For the case of an electrical short circuit at operational mode due to a failure in the generator or elsewhere, a high torque occurs on the shaft [1]. If there is no data about the short circuit torque, two times the design torque is a reasonable value for it.

$G=2.0$ (if no accurate data is available)

Bending moment on the shaft:

$M_{\textrm{x-shaft}}=GQ_{\textrm{design}}=28.68\,\textrm{N}$

$M_{\textrm{xB}}=\frac{M_{\textrm{x-shaft}}}{B}+m_{\textrm{B}}gR_{\textrm{cog}}=13.55\,\textrm{Nm}$

#### Load case G: Shutdown (Braking)

The use of a mechanical braking system on the drive train requires calculating the maximum torque on the shaft [1]. It can be assumed, that the maximum shaft torque is equal to the design torque from the rotor plus the designed braking torque, which was determined by the design team through calculations.

Bending moment on the shaft:

$M_{\textrm{brake}}=30.75\,\textrm{Nm}$

$M_{\textrm{x-shaft}}=M_{\textrm{brake}}+Q_{\textrm{design}}=45.09\,\textrm{Nm}$

$M_{\textrm{x-shaft}}=45.09\,\textrm{Nm}$

$M_{\textrm{xB}}=\frac{M_{\textrm{x-shaft}}}{B}+m_{\textrm{B}}gR_{\textrm{cog}}=17.65\,\textrm{N}$

There is no need to multiply the design torque by a factor of two, because the wind turbine design comprises a gearless drive.

For this load case it is assumed that the SWT and its parts are facing a 50-years-gust for 3 seconds. The main force is due to the drag when the turbine will be stationary parked [1].

Flap wise root bending moment (y-axis):

$C_{\textrm{d}}=1.5$
$V_{\textrm{e50}}=V_{\textrm{ref}}\cdot1.4=42\,\frac{\textrm{m}}{\textrm{s}}$
$V_{\textrm{ref}}=30\,\frac{\textrm{m}}{\textrm{s}}$

$M_{\textrm{yB}}=c_{\textrm{D}}\frac{1}{4}\rho V_{\textrm{e50}}^{2}A_{\textrm{proj,B}}R=63.21\,\textrm{Nm}$

The thrust load on the rotor shaft for a SWT can be calculated with the following equation:

Maximum thrust on rotor shaft:

$F_{\textrm{x-shaft}}=Bc_{D}\frac{1}{2}\rho V_{\textrm{e50}}^{2}A_{\textrm{proj,B}}=632.06\,\textrm{N}$

[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}
}