Appendix G: Sign convention for internal loads
1. General
The RIFLEX forces stored by SIMA are those internal to an element, directed along/about the element’s local axes.
If the stored force/moment is positive, it means the force/moment is directed as indicated by green arrows in Figure 1.
These values are not necessarily positive along/about the element’s positive local axes, this depends on whether values are extracted at node 1 or 2 of the element.
It should be noted that when extracting loads from a given element, only stiffness based loads for that element are included, inertial and damping loads of the particular element are not included. For submerged elements, or elements with internal contents, the effective tension is reported.
2. Transforming internal loads to the local coordinate system
If internal loads are to be represented as loads with signs consistent with the element’s local coordinate system (i.e. positive force directed along positive axis, positive moment directed based on right hand rule), the following sign transformations should be made:
Force/Moment  Node 1  Node 2 

\(F_x\) 
\(V_x\) 
\(V_x\) 
\(F_y\) 
\(V_y\) 
\(V_y\) 
\(F_z\) 
\(V_z\) 
\(V_z\) 
\(M_x\) 
\(Q_x\) 
\(Q_x\) 
\(M_y\) 
\(Q_y\) 
\(Q_y\) 
\(M_z\) 
\(Q_z\) 
\(Q_z\) 
3. Example
Consider one of the examples included in SIMA, accessed via Help::Examples::Wind Turbine::INO WINDMOOR semi 12 MW
, see Figure 2.
In Model::Calculation Parameters::Dynamic Calculation::Storage
,
modify:

Displacements
to ensure that displacements are stored for:
shaft3
(at least Segment 2, node 1) 
bl<i>foil1
(at least Segment 1, node 1), for i = 1, 2, 3


Force response
to ensure thatStore Transformation Matrices
is selected, and that internal forces are stored for:
shaft3
(at least Segment 2, element 1) 
bl<i>foil1
(at least Segment 1, element 1), for i = 1, 2, 3 
optionally:
bl<i>ecc1
(at least Segment 1, element 1), for i = 1, 2, 3

Consider the schematic of the shaft, blade eccentricity element, and first blade foil element, see Figure 3. sqwqheqowheqwhe
It is desired to extract loads at node 1 of the 1st foil element, convert them to the fixed shaft coordinate system, and compare to wind turbine aerodynamic loads, expressed in the same reference system. The procedure is outlined as follows:

For each blade \(i\), extract:

The internal loads at node 1:
\(V_{i}^b, \, Q_{i}^b\)

Convert from internal loads to loads in the local coordinate system (see the table shown earlier): \(V_{i}^b \rightarrow F_{i}^b, \, Q_{i}^b \rightarrow M_{i}^b\)
In Figure 3 the loads extracted at node 1, are the internal loads required to keep the element in equilibrium, i.e. those applied by the rest of the system to the element
. We are interested in the opposite, i.e. the loadsapplied by the element to the rest of the system
. Thus \(F_{i}^b = F_{i}^b, \, M_{i}^b = M_{i}^b\). If loads were e.g. extracted at node 2 of the eccentricity elementbl<i>ecc1
, they are already the desired loads, and no further modification is required 
The position of node 1 (in global system): \(p_{i}^g\)

Transformation matrix from local to global for element 1: \(T_{b,i}^g\)


For the fixed shaft element (Segment 2 of the shaft), extract:

The position of node 1(in global system): \(p_{s}^g\)

Transformation matrix from local to global for element 1: \(T_{s}^g\)


For each blade \(i\):

Define the offset from node 1 of the fixed shaft, to node 1 of the 1st foil element on each blade:
\(r_{i}^g = p_{i}^g  p_s^g\)

Convert forces and moments from local to global system:
\(F_{i}^g = T_{b,i}^g F_{i}^b\)
\(M_{i}^g = T_{b,i}^g M_{i}^b\)


Accumulate forces and moments from all blades at the fixed shaft node (expressed in global system):
\(F^g = \sum _{i} F_{i}^g\)
\(M^g = \sum _{i} M_{i}^g + r_{i}^g \times F_{i}^g\)

Convert forces and moments from the global to the fixed shaft coordinate system:
\(F^s = {T_{s}^g}^T F^g\)
\(M^s = {T_{s}^g}^T M^g\)
The results are are shown in Figure 4 and Figure 5, and can be compared to forces and moments stored with the Wind Turbine object.
The difference in torque (moment about the fixed shaft \(x\)axis) calculated from Riflex loads at the first blade nodes (Riflex: \(\vec{M} + \vec{r} \times \vec{F}\)) and generator torque at the low speed shaft (Gen. Torq. LSS) can be attributed to inertial loads of the first blade elements that are not included in the loads extracted from Riflex. Extracting loads at node 2 of the blade eccentricity elements instead, largely eliminates the observed differences, see Figure 6 and Figure 7.
The remaining large offsets between Riflex and aerodynamic loads visible in \(F_x\), \(F_z\) and \(M_y\) can be attributed to the mass of the rotor, this can be confirmed through some simple calculations:
Consider the mass of the rotor, \(m_{r} = 189397.0 \, \text{kg}\), and a shaft tilt of \(\theta = 6.0^\circ\).
In the shaft coordinate system, this implies
and
These numbers match up closely with the initial offsets seen in the figure Forces in the fixed shaft system. Lastly, the rotor centre of mass can be calculated ^{[1]} to be located approximately
(i.e. upwind) of node 1 on the fixed shaft element, implying
also closely matching the initial offset in the figure Moments in fixed shaft system.
Calculation Parameters::Static Calculation::Mass summary
.