3.3 Modal Filtering
The physical response spectrum is the result of a summation of individual modal responses. Spatial modal filtering can be applied to determine the values of the modal coordinates, or contribution from a subset of individual modes, at areas of interest in the operational response spectrum. In order to predict the fatigue and wear in components, modal filtering can be used to calculate the number of loading cycles and the magnitude of response each mode has undergone in operation. This has applications in cycle-based, predictive maintenance as well [9].
3.4 Modal Vector Selection and Modal Filter Verification
In order to improve the numerics of the calculation by having an overdetermined system, the number of modal vectors chosen for the filter should be less than the number of measurement channels, typically by a factor of two or more.Furthermore, the modal vectors should be linearly independent so that they can be distinguished spatially [9]. The polyreference time domain (PTD) algorithm along with a consistency diagram approach was employed to identify physical, stable poles and vectors in the modal impact data. A modal assurance criterion (MAC) test was then performed to check the modal vectors for linear independence. There were 12 response channels, and four modes were chosen, corresponding to frequencies of 5.0, 42.7, 47.0, and 54.3 Hz. The low off-diagonal values of the MAC in Fig. 29.10ademonstrate the independence of the modal vectors.
Next, to verify the operation of the modal filter, a shaker test was performed. A small, seven-pound electro-dynamic shaker excited one of the rotor blades in the flap-direction shown in Fig.29.10bwith a sinusoidal input at each of the resonant frequencies used in the modal filter. The modal filter was then applied to the time response data from the accelerometers, and was able to extract the modal coordinate of the mode being excited. The modal coordinates for each test were summed and plotted in Fig. 29.11below.
The filter was then applied to the operational data. The matrix representation of the modal filter in (29.2) can also be formulated in the frequency domain and evaluated at every frequency in the response spectra. The wind turbine operational data was analyzed in this way. In particular, the modal coordinates were computed at the peaks in the summed OMA FRF response spectrum of all 12 measurement channels for each wind speed and shear condition. A sample result is shown in Fig.29.12below, which shows the magnitude of the modal coordinates at each of those peaks. To view the average value of the modal coordinates as a function of shear condition, the magnitude of each modal coordinate was summed at each of the peaks in the OMA response spectrum, then normalized for each wind shear.The results for the 35 Hz fan speed (3.4 m/s wind speed at no-shear) are shown in Fig.29.13below.Clearly, the 47 Hz mode is dominant regardless of wind shear; however, the response of the remaining three modes does appear to depend on shear condition. The 5 Hz mode is of particular interest since it represents some considerable shaft vibration, which may introduce dynamic fatigue loads on the rotor bearings. The vertical shear condition, which will be predominant on the building rooftop, contains the highest contribution from the 5 Hz mode. Additionally, each shear condition has a higher normalized 5 Hz modal coordinate response than the baseline no-shear condition.
4 Conclusion
Several modal impact tests were performed on a small vertical axis wind turbine (VAWT). A telescopic roof-fixture was designed and built for future operational testing to explore the effects on the structural dynamic response of the wind turbine in sheared and turbulent wind flow in urban locations. Modal tests of the turbine were conducted for a range of azimuth angles and three different extended heights of the tower, resulting in a considerable shift downward in resonant frequencies for tower-coupled modes at extended heights, and relatively little change depending on azimuth position. The azimuth tests may have been less successful than anticipated in exciting the blades and struts in the directions intended: perpendicular to the tower base in six different orientations from 0 to 120°of rotation. The roving accelerometer test, as opposed to roving input, may also have decreased the quality of the results.
Operational data was recorded for a range of wind speeds and wind shear conditions with the VAWT installed in a wind-dynamics test bed under controlled wind-input conditions. A modal filtering technique was applied and verified using a shaker-test. The modal filtering results indicated significant changes in modal response among the different wind shear conditions. Future work will apply modal filtering to the operational response of the turbine installed on the laboratory roof.
Loading cycles and magnitudes will be counted, and any changes in the performance of the turbine will be documented. Additionally, noise measurements will be taken to correlate modal response to structural noise emissions.
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