Structural Calculations of Part 1

inner, passive part of the blade in (4.44). Out of these two values the overall CoG is determined in the following manner:

r_blade=

( (

)

(

) )

m_blade ^(4.46)

r_blade Overall CoG of the blade [m]

Now, after the integration values for the hub has been utilized following the conclusion of the sequence in Figure 4.6, and the bending moments due to torque and thrust accordingly have been determined, a for-loop identical to the third for-loop in that figure is encountered. In this loop is the rotor angle the loop variable, and the following values are calculated for the hub attachment: Shear force and bending moment in the rotor plane due to torque and gravity, and total normal force due to inertia and gravity. The corresponding results are appended in “Loads_and_zentroids1” for each rotor angle in the same way as for the blade elements, as shown in Figure 4.7.

q1 connected to each other, so that a continuous q1 exists for the whole torque box at the current rotor angle. This means e.g. that the end result from the upper flange is added to the start result for the front spar, and so on. Following the completion of q1 is this printed to the file “q1_1.txt”. A simplified overview of this sequence can be seen in Figure 4.8:

Figure 4.8: Details to program sequence for structural calculations

In the next sequence will the constant shear flow, q0, and the SC be calculated:

The SC, being a geometric value, is calculated for each blade element, while q0

is calculated for each blade element at each rotor angle. In the program, this is done by letting the compiler run through three for-loops identical to those of the previous sequence, controlled by the number of elements, the rotor angle and the torque box variable respectively. In the inner for-loop is the calculation for q0

prepared through numeric integration of q1, ref. 2.5.3 equation (2.93). By the completion of this for-loop, runs the compiler further through the for-loop controlled by the rotor angle, and (2.93) can be executed, and the value for q0

identified. Through an if-query, which only applies for the first rotor angle for each blade element, is now the distance between the torque box CoG and the SC in x-direction calculated, ref. 2.5.3 equation (2.97). The last action in this sequence is the printing of the result for q0 to the file “q0_1.txt”. The structure of this sequence can be studied in Figure 4.9:

Figure 4.9: Overview of program sequence for calculations on the torque box

In the third and final sequence are the total shear flows calculated, and the complete loading for each position in the torque box, at each rotor angle and for each blade element is hence being identified. This whole sequence is executed once for each side of the torque box, to make the calculations and coding more transparent. Following the calculations of the shear flows are also the normal, shear and comparative stresses calculated.

This sequence is roughly built up in the same manner as the two previous ones, with the same three for-loops. The resulting force flows and stresses are calculated inside the third for-loop, but directly after entering the first for-loop are the deviations for the 0.5c point of the current blade element and the 0.5c points for the effective force arms being calculated, ref. 2.5.3, equation (2.95), and Figure 2.15. These calculations are done for the effective arms of the shear forces from gravity and thrust, and are necessary as they intersect the 0.5c line, (at the height/z-value of the SC) and because the 0.5c line has a sweep along the blade radius. This leads to the occurrence of a distance in the x-direction between the 0.5c point in the blade element and the 0.5c point at the location of the resulting shear forces from gravity and thrust.

With the deviations between the 0.5c points now identified, it is possible to calculate the shear flows due to the torsion from the shear forces that do not have their line of forces through the SC, and thereby the total shear flows.

Moving to the third for-loop is now the total shear flow for the current blade element, at the current rotor angle and at the current position in the applicable torque box wall calculated, ref. 2.5.3 equations (2.94) - (2.98). Directly after this are the comparative stresses calculated, ref. 2.5.3 equations (2.107) - (2.109).

With the shear- and normal flows/stresses and the comparative stresses identified, starts now a screening process of these values, and the highest values of shear stress, tensional/compressive stress and the three comparative stress types are identified, and linked with the number of element, rotor angle and position in the torque box wall. During the sequence for the rear spar, which is the last of the walls being calculated, are the results for the overall shear flow

at this point printed to the file “qs_1.txt”. With the conclusion of the sequences are then the results from the screening of the stress values printed to

“Stress_analysis1.txt”. These sequences are reconstructed in Figure 4.10:

Figure 4.10: Final calculations for force flows and stresses in the torque box

At this point are all the calculations for the first part of the program completed, and all the results stored in the files mentioned in this subchapter. A message is now conveyed in the user window, that part 1 has been completed, with the applicable result for the power generated at the design conditions. Now, the user has the choice of executing part 2 of the program by pressing “2”, or part 3 by pressing “3”.