Second prototype

For the second prototype, the entire structure was strengthened by increasing wall thickness and adding support. In addition, the holes through the sides are sized to accommodate threaded inserts. These brass inserts have coarse threads on the outside, which are suitable for plastic, and fine machine threads on the inside which allows the use of socket head set screws to be used for fastening the wire. The beefier sides of the frames means that the new mount is larger than the old one. The difference has in part been compensated for by decreasing the amount of space between the inner and outer frame, from 15mm to 10mm. This means the size of the vibration’s amplitude the camera mount can handle is reduced. This should not be a problem since the expected amplitude is far less than ±10mm.

(a) Rendering of the second prototype. (b) The finished part. Figure 9.14: Designing and printing a new camera mount, second prototype.

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The amount of mounting holes for wire have been reduced relative the first prototype. To increase strength in the corners of the large frame, there are no longer more holes in the large frame than in the small one. From the first prototype it was discovered that wire loops centered around the corners of the frames appeared to have no additional damping effect, only providing additional stiffness to the damping system. To get a better understanding of the properties of a wire damper like this, one could model the system as simple mass-spring-damper systems in each directions given by

X F = c ˙x + kx− fv = m¨x m ¨ x+2ζω0˙x + ω20 = 1 mfv, (9.1)

where m is the mass, c is the damping constant, k is the spring stiffness constant (Hook’s law) and fv is the force induced by vibrations. ω0 =

q

k

m is the system’s natural frequency while

ζ = c

2√km is the damping ratio. From this, the damping system’s transfer functions (in each direction) are given by

X Fv (s) = 1 m s2_{+ 2ζω} 0s + ω02 . (9.2)

The UAV’s engine is operating within the interval of 2000-7000 RPM, which means the induced vibrations would be within the frequency spectre given by ωv ∈ [33.33, 116.67] Hz. Since the natural frequency in a mass-spring-damper system can be seen as the cut-off frequency in a low-pass filter, the natural frequency of the mass-spring-damper system should be below 33.33Hz to avoid the wire damper to vibrate in harmony with the rest of the UAV. In addition, the system should be slightly over-damped, ζ > 1, to provide smooth motions that would not impair the camera image quality.

Figure 9.15 present a bode plot of a mass-spring-damper system with a damping ratio of 1.1 and natural frequencies of 10Hz, 20Hz and 30Hz. From the magnitude plot one can clearly see that a system with ω0 of 30Hz would be quite stiff in conjunction with the system where

ω0 is 10Hz. We want the camera to move in a smooth motion, which means that the wire

damping system should have a natural frequency below 30Hz and closer to 10Hz. In order to develop a suitable wire damper for the still camera, one should use a controlled vibration rig where different wires and wire settings are tested. Simply examining the images from the camera, while being subjected to different frequencies of induced vibrations, should give a good indication of the capabilities of the different wire damper configurations. Also, by using suitable sensors, e.g. accelerometers, mounted on the wire damper one could construct bode plots (transfer functions) from the test results. The natural frequencies for the different designs could be read from the bode plots where the phase plot reaches −90◦_{. Also the damping}

ratio could be found from a bode plot (Nasir, 2009). Unfortunately, we do not have access to equipment needed to perform these tests, which means the wire damper’s stiffness should be examined and flight tests should be conducted to check the camera image quality.

152 9.5. Still camera −160 −140 −120 −100 −80 −60 Magnitude (dB) 10−1 100 101 102 103 −180 −135 −90 −45 0 Phase (deg)

Mass (m) =1kg, Damping ratio (ζ) =1.1

Frequency (Hz)

ω₀ =10Hz ω₀ =20Hz ω

0 =30Hz

Figure 9.15: Bode plots of a mass-spring-damper system.

Multiple wire designs were developed and examined to check the wire-dampers stiffness. Bicycle brake wire from a local hardware store was tested using multiple wire layouts, however the wire-damper became too stiff. Images from different layouts using brake wire can be found in appendix B.4. The simple tests conducted suggest the 1.5mm electrical wire, configured as shown in figure 9.16, is the most suitable for this application.

(a) The camera damper seen from the right side. (b) The camera damper seen from the top. Figure 9.16: Final wire configuration with 1.5mm electrical wire.

In addition to the wire damper being developed and tested, some commercially available rubber damping balls were acquired to provide a reference for comparison for the damping properties

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of the wire system. These rubber balls come in several versions depending on the weight of the camera mounted on them. The wire damper and rubber balls could possibly be used together for enhanced performance. If further tests are to be conducted, the use of a controlled vibration rig would be preferable. Most of the tests performed in this section are based on guesswork and are greatly simplified. It is safe to assume that flight testing every version and each improvement is plainly infeasible.