Experiments with Supersonic Beams as a Source of Cold Atoms
Experiments with Supersonic Beams as a Source of Cold Atoms
Experiments with Supersonic Beams as a Source of Cold Atoms
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Figure 3.12: Finite element calculation <strong>of</strong> rotor vibrational modes. This w<strong>as</strong> performed<br />
using the built in finite element package in Solid Edge. The vibrational mode<br />
shown h<strong>as</strong> a resonance frequency <strong>of</strong> 47Hz. The calculation does not take into account<br />
the fact that the rotor and spindle are made from different materials, <strong>as</strong> only one material<br />
can be simulated. As such the entire structure is simulated <strong>as</strong> stainless steel,<br />
since most <strong>of</strong> the weight is in the stainless steel spindle. Additionally, the shaft <strong>of</strong> the<br />
spindle, which is found to be region that flexes most, is stainless steel. Reducing the<br />
weight <strong>of</strong> the rotor (it is titanium in the experiment) would likely result in a slightly<br />
higher resonant frequency in the real system.<br />
in black. The d<strong>as</strong>hed lines indicate resonances by at le<strong>as</strong>t one <strong>of</strong> these methods. Ad-<br />
ditionally, these resonances can be heard <strong>as</strong> incre<strong>as</strong>ed noise from the chamber, and<br />
the chamber vibrations are e<strong>as</strong>ily felt by placing a hand on the chamber. The solid<br />
lines in figure 3.11 are Lorentzian fits <strong>of</strong> the limiting resonance, which is predicted<br />
be lie around 48 − 50 Hz. From these fits, the peak vibrational amplitude can be<br />
estimated to be 1000 − 2000 μm which is too large to be comfortably p<strong>as</strong>sed through,<br />
and thus limits the rotor velocity to 42 Hz.<br />
A finite element calculation <strong>of</strong> the vibrational modes <strong>of</strong> the rotor and spindle<br />
w<strong>as</strong> performed to investigate the source <strong>of</strong> this unexpected resonance using the built<br />
in finite element package <strong>of</strong> CAD program Solid Edge. This analysis shows the nature<br />
<strong>of</strong> the resonance which limits the rotor velocity, and the results <strong>of</strong> this calculation are<br />
shown in figure 3.12. The finite element calculation predicts two pendulum modes,<br />
one at 34 Hz and one at 47 Hz, in addition to a twisting mode at 35 Hz. Several<br />
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