Fixed on One End
Due to the fact that the mechanosensory hairs which were studied, as described in Sec- tion 4.5, lack the integrated actuator associated with the micro-cantilever switches described in the previous section, an external excitation source was needed. Since these hairs respond
Table 4.2: Wire dimensions and properties
Dimensions and Properties Value
Nominal Lengths (mm) 12, 16, 20 Measured Lengths (mm) 11.74, 16.22, 19.22
Diameter (µm) 33
Material Copper Young’s Modulus (GPa) 110
Density (kg/m3) 8970
to air motion in nature, this was a natural choice. Since the cercal hairs are somewhat chal- lenging to work with, initial testing of this methodology was done using a wire. This wire, a magnet wire approximately 33µmin diameter, was treated as a uniform circular cantilever,
of pure copper. Lengths were selected to produce first natural frequencies on the order ex- pected for the mechanosensory hairs, which were primarily in the 50 - 100 Hz range [35]. The measured dimensions and assumed properties of the wire are listed in Table 4.2. The wire was excited with air motion, generated using a loudspeaker in the near field. Details of this excitation are described in Subsection 4.4.1. The wire was positioned under the micro- scope objective and above the speaker on a support of lab frame, and positioned using an X-Y stage moved by attached micrometers. The apparatus is described in further detail in Subsection 4.4.2. Details of the measurements taken and analysis performed are presented in Subsection 4.4.3
4.4.1
Excitation for SSI-Based Modal Analysis of Wire Segments
To apply the stochastic subspace identification algorithm implemented in MACEC it is necessary to apply a white noise excitation over the frequency range of interest. To do this in the low frequency range at which the mechanosensory hairs, and thus the wires selected for testing, have their first resonant frequency a subwoofer is needed. The speaker chosen, an Earthquake sound SWS-8 automotive subwoofer, is a shallow mount speaker, with a resonant frequency of 30 Hz when unmounted [53]. This speaker was paired with a JBL automotive subwoofer amplifier model GT5-A3001. A box to contain the subwoofer and fit under the vibrometer microscope was constructed, and the speaker was installed therein. The amplifier was powered using a Kepco variable output DC power supply set to provide 12 V, and provided with a signal from the signal generator card in the Polytec DMS, described in Section 4.2. A test of the frequency response of the speaker/amplifier pair was performed, and the resulting frequency response curve is shown here in Figure 4.5. The speaker response shows a fairly smooth curve, peaking around 60 Hz, and falling off
CHAPTER 4. SSI APPARATUS & METHODOLOGY 60
Figure 4.5: Frequency response of speaker / amplifier pair
gradually as frequency increases. The main range of interest, between 40 and 120 Hz, shows fairly small variation in amplitude, which should not cause major error in analysis. The signal applied was a sequence of normally distributed random numbers, generated in MATLAB, and band-pass filtered with a passband of 20 to 350 Hz, using a type II Chebyshev filter. This frequency range is suitable for the speaker and amplifier providing the excitation and covers the range of interest.
4.4.2
Support and Positioning for SSI-Based Modal Analysis of Wire
Segments
The wire, and later the cricket cercus, was attached to a small piece of stiff piano wire using cyanoacrylate glue, as shown in Figure 4.6. This was then secured with tape to a support made from a section of lab frame, which was glued to a heavy base, shown in Figure 4.7. This was placed on an X-Y positioning stage on the vibration isolation table beside the vibrometer and the speaker enclosure. A photograph is shown in Figure 4.8. This stage was used for fine positioning of the wire under the vibrometer, and also, due to the length of the wire being greater than the vibrometer’s field of view, for performing the scan, allowing measurements to be taken along the entire free length of the wire. The stage was moved using attached micrometers with resolution of 0.001 inches, or approximately 25.4µm.
Figure 4.6: Test wire mounted for experiment
CHAPTER 4. SSI APPARATUS & METHODOLOGY 62
Figure 4.8: Vibrometer setup for air excited experiments. A) DMS PC; (B) vibrometer controller; (C) microscope with vibrometer scanning attachment; (D) scan controller; (E) subwoofer amplifier; (F) enclosed subwoofer; (G) specimen support; (H) vibrometer sensor unit
4.4.3
Measurements and Analysis for SSI-Based Modal Analysis of
Wire Segments
At each of nine points (eight on the 20 mm wire) between the tip and the base of the wire a set of time domain vibration measurements was made. Because these measurements were made at points along the entire length of the wire, no fixed reference structure was avail- able, and thus the measurements were made in single point (non-differential) mode, with the reference fiber attached to a fixed mirror. The sampling rate was 5120 samples per sec- ond and three sets of 16384 samples were collected at each point. The measurements were made with a low pass filter at 2 kHz, using the highest quality option in the PSV software. This data was exported from the Polytec PSV software, and then loaded in MATLAB and formatted for MACEC. The data was imported to MACEC, where it was detrended, deci- mated by a factor of four, and analyzed using SSI. An Euler-Bernoulli analysis of the wire was also done, to predict expected natural frequencies for comparison. The results of these analyses are described in Chapter 6.
Figure 4.9: Cricket cercus attached to stiff wire. Some of the larger mechanosensory hairs are visible in the photograph.