1

APX-45 rotor blade

Two superelement approximation

Figure 4.7: Schematic of the APX-45 rotor blade and its two superelement approximation, with O: 2 degrees of freedom rotational joints.

• The blade structural properties in reality differ from their designed values due to uncertain material parameters and manufacturing tolerances. The APX-45 rotor blades are produced by moulding processes using composite materials of which the material properties are not known exactly. The upper and lower blade surfaces are manufactured separately in two moulds by hand-lay-up, and joined together using high strength adhesives. The result being that the blade mass and blade dimension are not precisely controllable;

• Quality of the applied experiments and determination of the eigenfrequencies from the measurements are not adequate. The natural frequencies of the APX-45 rotor blade have been determined from hand-excited displacement measurements in both lead-lag and flap direction. The displacements were measured at two locations using LVDT's (linear variable differential transducers);

• The flexibility of the test stand in which the blade has been mounted during the modal testing can not be neglected.

When the frequency errors for the first three flap and lead-lag eigenfrequencies of the superelement approximation are calculated relative to the eigenfrequencies as computed by FAROB, they converge to zero. It should be noted that the FAROB approximation also divides the blade in beam elements, but requires a significantly higher (> 100) number of elements. This illustrates (again) the power of the superelement approach.

Finally, the Finite Element program MARC [176] will be used to check whether the model assumptions are violated. The finite element mesh has been generated using the aforementioned blade definition file. The elements are eight noded, thick shell elements with 6 degrees of freedom at each node (MARC element type 22). The

1st Flap

Figure 4.8: The relative errors for the first two flap and lead-lag non-rotating eigenfrequencies of the APX-45 rotor blade as function of the number of superelements Nse. Dashed-dotted horizontal lines: + 2% and -2% error bound respectively.

1st Flap

Figure 4.8: The relative errors for the first two flap and lead-lag non-rotating eigenfrequencies of the APX-45 rotor blade as function of the number of superelements Nse. Dashed-dotted horizontal lines: + 2% and -2% error bound respectively.

elements have a composite layer structure. The layers of the composite are composed of orthotropic material. The total model contains 3137 elements, and 3055 nodes resulting in 18330 degrees of freedom. The first 15 eigenfrequencies were calculated using the Lanczos eigenvalue extraction algorithm. The resulting frequency errors of the first two flap and lead-lag eigenfrequencies of the APX-45 rotor blade are listed in the second column of Table 4.4.

APX-45 rotor blade

Mode

Difference Nse = 6 w.r.t. SL-DUT measurements

Difference MARC w.r.t. SL-DUT measurements

1si flap 1si lead-lag

- 12.6%

Table 4.4: Comparison of the first two flap and lead-lag non-rotating rotor blade eigenfrequencies calculated using the superelement approximation for Nse = 6 (left) and MARC (right) to the ones from a full-scale modal test performed by the Stevin Laboratory of Delft University of Technology (SL-DUT).

Table 4.4: Comparison of the first two flap and lead-lag non-rotating rotor blade eigenfrequencies calculated using the superelement approximation for Nse = 6 (left) and MARC (right) to the ones from a full-scale modal test performed by the Stevin Laboratory of Delft University of Technology (SL-DUT).

It can be concluded that the effect of violating the model assumptions is probably negligible, but that the quality of the model is either limited by the quality of the input, or by the quality of the applied experiments and resulting eigenfrequency determination. In the next subsection we will further investigate the cause of the observed bias by examining an APX-70 rotor blade.

Renewable Energy Eco Friendly

Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

Get My Free Ebook


Post a comment