Environmental Engineering Reference
In-Depth Information
Table 11-1.
Modal Frequencies of the Non-Rotating 2-m VAWT
[Carne
et al.
1982]
Mode
Number
Mode name
Test
Initial
model
(Hz)
Tuned
model
(Hz)
Tuning
change
(Hz)
(Hz)
1
1st Anti-Symmetric Flatwise
12.3
12.5
12.3
-1.6%
2
1st Symmetric Flatwise
12.5
12.6
12.4
-1.6%
3
1st Rotor Out-of-Plane
15.3
17.1
15.2
-11.1%
4
1st Rotor In-Plane
15.8
17.2
15.9
-7.6%
5
Dumbbell
24.4
22.6
24.4
+8.0%
6
2nd Rotor Out-of-Plane
26.2
30.5
26.2
-14.1%
7
2nd Rotor In-Plane
28.3
30.6
28.0
-8.5%
8
2nd Symmetric Flatwise
29.7
30.9
30.6
-1.0%
9
2nd Anti-Symmetric Flatwise
31.5
39.7
31.7
-20.2%
10
3rd Rotor Out-of-Plane
36.5
42.3
36.5
-13.7%
Calculated Rotating System Modes
The Campbell diagram in Figure 11-9 presents the modal frequencies of the 2-m
VAWT at rotor speeds from 0 to 600 rpm. The curves in this figure are the calculated
frequencies obtained using the tuned NASTRAN model, with mode numbers corresponding
to those in Table 11-1. The variations of the frequencies with rotor speed are quite complex.
While most increase monotonically with speed, some decrease monotonically. Others
increase and then decrease and
vice versa.
These variations are similar to those associated
with the classical whirling-shaft problem. In addition to complicated frequency variations,
the mode shapes also change in character with rotor speed. Specifically, mode shapes
which are completely
uncoupled
when the turbine is parked become coupled during rotation.
This coupling is discussed in more detail in Carne
et al.
[1982]. In mathematical terms, the
modes change from real to complex as the turbine rotates.
Sample Experimental Modal Analysis
An overview of the general techniques for modal testing of wind turbines will now be
presented, again using the Sandia/DOE 2-m VAWT as an example. Portable data acquisi-
tion tools of the test engineer are based on
the fast Fourier transform.
The FFT technique,
which involves exciting the structure with a force having a linear spectrum containing the
frequency band of interest, is generally faster and more versatile than the classical
swept-
sine
technique. The applied forces and responses are measured in the time domain and
transformed to the frequency domain using the FFT. The frequency response functions are
then computed from the cross-spectral and auto-spectral densities of the applied force and
the responses.
Typically, several measurements are averaged to reduce the effects of uncorrelated
noise. A more-complete description of FFT modal testing is contained in [Klosterman and
Zimmerman 1975]. The greater versatility of this technique is a result of its more-relaxed
requirements on the excitation force. For example, the FFT technique is equally applicable
to shaker-driven excitations, instrumented-hammer impacts, and excitations by wind forces.
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