12 A Cost Effective DIC System for Measuring Structural Vibrations 145 Fig. 12.5 Operation deflection shapes (ODS) of a vertically excited elastic rotor at (a) 103 Hz and (b) 139Hz (c) Deformation of a quadcopter rotor due to aerodynamic forces a 3900 rpm Next, the deformation of an elastic rotor of 250 mm length and a maximal width of 40 mm due to vertical shaker excitation is studied. Again, this is a very light structure and the use of contactless measurement techniques is obligatory. This time, the random pattern is printed on a self adhesive film and transferred to the moderately curved rotor. Although the rotor represents a kind of slender, beam type structure, the DIC displacement analysis works satisfactorily, see Fig. 12.5a, b, where the measured operation deflection shapes at frequencies of f D103Hz and f D139Hz are illustrated. As before, the stereo image acquisition was performed using standard webcams with fa D0:1Hz. The results indicate excellent full field measurements which can be easily interpreted, and furthermore, interesting deflection properties like, e.g. nodal lines can be extracted directly. In the last example the deflections of an elastic quadcopter rotor due to aerodynamic forces were analyzed during normal operation. The quadcopter was fixed to a test rig while performing an engine run-up between 1900 and 4000 rpm. Because the rotor was in permanent rotation, the triggering of the stroboscopic light had to be synchronized to the rotation angle using a simple laser light barrier. Due to the high velocity of the rotor tip, the duration of the stroboscopic light flash was reduced to less than 2 s and thus the illumination level was low. Consequently, relatively long expose times were necessary for good quality imaging. Again, all measurements were taken with the calibrated webcams in stereo configuration. In Fig. 12.5c the rotor deformation is given for 3900 rpm. Apparently, the rotor tip is raised to approximately 2 mm. Of course, the vertical lift of the rotor as a function of the rpm can be visualized in a computer animation. Additionally, the curvature of the rotor is clearly visible because the dynamic DIC renders both, the static geometry and the dynamic deflections. Looking at these results, it is possible to conclude, that the low cost stereo-DIC system has performed well during experimental testing. All calculations have been performed using standard Matlab code, partly optimized for matrix calculations and thus possible parallel processing. When limiting the analysis to several hundred virtual measurement points, and working with image frame rates in the range of 2–5 Hz, the analysis was performed in real-time. With respect to measurement accuracy, the system is also performing well. Commercial DIC systems define the displacement resolution by the ratio e D s=l of measurement accuracy s over the length of the visible image section l. Depending on the image acquisition system, usual values are in the range of eh D 1=50000 up to eh D 1=100000 for horizontal (inplane) measurements. Depending on the distance and orientation of stereo vision system this value is reduced for vertical (out of plane) measurements by a factor between 2 and 3. Experiments with the proposed system indicate a vertical accuracy measure of ev D1=10000. In the setup used, the webcams lenses have turned out to be the limiting factor since there are no variable settings and depth of field, focus and measurement range cannot be changed. 12.5 Conclusions The work presented proves that standard webcams combined with an innovative lighting concept can be used to precisely measure dynamic structural displacements. Using stroboscopic light, the actual frequency of a periodic high frequency oscillation is shifted to the low image acquisition rate of the cameras applied. All vibration measurements indicate that the proposed system has exceeded the expectation with respect to flexibility and accuracy. When compared to high end
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